CINXE.COM

<!DOCTYPE html> <html lang="en" dir="ltr"> <head>  <script async src="https://www.googletagmanager.com/gtag/js?id=G-P63WKM1TM1"></script> <script> window.dataLayer = window.dataLayer || []; function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-P63WKM1TM1'); </script>  <script type="text/javascript" > (function(m,e,t,r,i,k,a){m[i]=m[i]||function(){(m[i].a=m[i].a||[]).push(arguments)}; m[i].l=1*new Date(); for (var j = 0; j < document.scripts.length; j++) {if (document.scripts[j].src === r) { return; }} k=e.createElement(t),a=e.getElementsByTagName(t)[0],k.async=1,k.src=r,a.parentNode.insertBefore(k,a)}) (window, document, "script", "https://mc.yandex.ru/metrika/tag.js", "ym"); ym(55165297, "init", { clickmap:false, trackLinks:true, accurateTrackBounce:true, webvisor:false }); </script> <noscript><div><img src="https://mc.yandex.ru/watch/55165297" style="position:absolute; left:-9999px;" alt="" /></div></noscript>    <title>Search results for: Ordinary differential equations</title> <meta name="description" content="Search results for: Ordinary differential equations"> <meta name="keywords" content="Ordinary differential equations"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> <button class="d-block d-lg-none navbar-toggler ml-auto" type="button" data-toggle="collapse" data-target="#navbarMenu" aria-controls="navbarMenu" aria-expanded="false" aria-label="Toggle navigation"> <span class="navbar-toggler-icon"></span> </button> <div class="w-100"> <div class="d-none d-lg-flex flex-row-reverse"> <form method="get" action="https://waset.org/search" class="form-inline my-2 my-lg-0"> <input class="form-control mr-sm-2" type="search" placeholder="Search Conferences" value="Ordinary differential equations" name="q" aria-label="Search"> <button class="btn btn-light my-2 my-sm-0" type="submit"><i class="fas fa-search"></i></button> </form> </div> <div class="collapse navbar-collapse mt-1" id="navbarMenu"> <ul class="navbar-nav ml-auto align-items-center" id="mainNavMenu"> <li class="nav-item"> <a class="nav-link" href="https://waset.org/conferences" title="Conferences in 2024/2025/2026">Conferences</a> </li> <li class="nav-item"> <a class="nav-link" href="https://waset.org/disciplines" title="Disciplines">Disciplines</a> </li> <li class="nav-item"> <a class="nav-link" href="https://waset.org/committees" rel="nofollow">Committees</a> </li> <li class="nav-item dropdown"> <a class="nav-link dropdown-toggle" href="#" id="navbarDropdownPublications" role="button" data-toggle="dropdown" aria-haspopup="true" aria-expanded="false"> Publications </a> <div class="dropdown-menu" aria-labelledby="navbarDropdownPublications"> <a class="dropdown-item" href="https://publications.waset.org/abstracts">Abstracts</a> <a class="dropdown-item" href="https://publications.waset.org">Periodicals</a> <a class="dropdown-item" href="https://publications.waset.org/archive">Archive</a> </div> </li> <li class="nav-item"> <a class="nav-link" href="https://waset.org/page/support" title="Support">Support</a> </li> </ul> </div> </div> </nav> </div> </header> <main> <div class="container mt-4"> <div class="row"> <div class="col-md-9 mx-auto"> <form method="get" action="https://publications.waset.org/search"> <div id="custom-search-input"> <div class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value="Ordinary differential equations"> <input type="submit" class="btn_search" value="Search"> </div> </div> </form> </div> </div> <div class="row mt-3"> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Commenced</strong> in January 2007</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Frequency:</strong> Monthly</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Edition:</strong> International</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Paper Count:</strong> 1829</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: Ordinary differential equations</h1> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1829</span> Numerical Treatment of Block Method for the Solution of Ordinary Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=A.%20M.%20Sagir">A. M. Sagir</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>Discrete linear multistep block method of uniform order for the solution of first order initial value problems (IVPs) in ordinary differential equations (ODEs) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. Furthermore, a stability analysis and efficiency of the block method are tested on ordinary differential equations, and the results obtained compared favorably with the exact solution.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Block%20Method" title="Block Method">Block Method</a>, <a href="https://publications.waset.org/search?q=First%20Order%20Ordinary%20Differential%20Equations" title=" First Order Ordinary Differential Equations"> First Order Ordinary Differential Equations</a>, <a href="https://publications.waset.org/search?q=Hybrid" title=" Hybrid"> Hybrid</a>, <a href="https://publications.waset.org/search?q=Self%20starting." title=" Self starting. "> Self starting. </a> </p> <a href="https://publications.waset.org/9997352/numerical-treatment-of-block-method-for-the-solution-of-ordinary-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/9997352/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/9997352/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/9997352/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/9997352/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/9997352/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/9997352/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/9997352/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/9997352/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/9997352/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/9997352/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/9997352.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">2794</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1828</span> On the Approximate Solution of Continuous Coefficients for Solving Third Order Ordinary Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=A.%20M.%20Sagir">A. M. Sagir</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>This paper derived four newly schemes which are combined in order to form an accurate and efficient block method for parallel or sequential solution of third order ordinary differential equations of the form y''' = f(x, y, y', y''), y(α)=y<sub>0</sub>, y'(α)=β, y''(α)=η with associated initial or boundary conditions. The implementation strategies of the derived method have shown that the block method is found to be consistent, zero stable and hence convergent. The derived schemes were tested on stiff and non – stiff ordinary differential equations, and the numerical results obtained compared favorably with the exact solution.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Block%20Method" title="Block Method">Block Method</a>, <a href="https://publications.waset.org/search?q=Hybrid" title=" Hybrid"> Hybrid</a>, <a href="https://publications.waset.org/search?q=Linear%20Multistep" title=" Linear Multistep"> Linear Multistep</a>, <a href="https://publications.waset.org/search?q=Self%20starting" title=" Self starting"> Self starting</a>, <a href="https://publications.waset.org/search?q=Third%20Order%20Ordinary%20Differential%20Equations." title=" Third Order Ordinary Differential Equations. "> Third Order Ordinary Differential Equations. </a> </p> <a href="https://publications.waset.org/9997258/on-the-approximate-solution-of-continuous-coefficients-for-solving-third-order-ordinary-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/9997258/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/9997258/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/9997258/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/9997258/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/9997258/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/9997258/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/9997258/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/9997258/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/9997258/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/9997258/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/9997258.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1769</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1827</span> Parallel Block Backward Differentiation Formulas For Solving Large Systems of Ordinary Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Zarina%20Bibi">Zarina Bibi</a>, <a href="https://publications.waset.org/search?q=I."> I.</a>, <a href="https://publications.waset.org/search?q=Khairil%20Iskandar"> Khairil Iskandar</a>, <a href="https://publications.waset.org/search?q=O."> O.</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, parallelism in the solution of Ordinary Differential Equations (ODEs) to increase the computational speed is studied. The focus is the development of parallel algorithm of the two point Block Backward Differentiation Formulas (PBBDF) that can take advantage of the parallel architecture in computer technology. Parallelism is obtained by using Message Passing Interface (MPI). Numerical results are given to validate the efficiency of the PBBDF implementation as compared to the sequential implementation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Ordinary%20differential%20equations" title="Ordinary differential equations">Ordinary differential equations</a>, <a href="https://publications.waset.org/search?q=parallel." title=" parallel."> parallel.</a> </p> <a href="https://publications.waset.org/3114/parallel-block-backward-differentiation-formulas-for-solving-large-systems-of-ordinary-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/3114/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/3114/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/3114/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/3114/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/3114/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/3114/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/3114/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/3114/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/3114/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/3114/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/3114.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1668</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1826</span> On the Efficiency of Five Step Approximation Method for the Solution of General Third Order Ordinary Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=N.%20M.%20Kamoh">N. M. Kamoh</a>, <a href="https://publications.waset.org/search?q=M.%20C.%20Soomiyol"> M. C. Soomiyol</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this work, a five step continuous method for the solution of third order ordinary differential equations was developed in block form using collocation and interpolation techniques of the shifted Legendre polynomial basis function. The method was found to be zero-stable, consistent and convergent. The application of the method in solving third order initial value problem of ordinary differential equations revealed that the method compared favorably with existing methods.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Shifted%20Legendre%20polynomials" title="Shifted Legendre polynomials">Shifted Legendre polynomials</a>, <a href="https://publications.waset.org/search?q=third%20order%20block%20method" title=" third order block method"> third order block method</a>, <a href="https://publications.waset.org/search?q=discrete%20method" title=" discrete method"> discrete method</a>, <a href="https://publications.waset.org/search?q=convergent." title=" convergent. "> convergent. </a> </p> <a href="https://publications.waset.org/10010422/on-the-efficiency-of-five-step-approximation-method-for-the-solution-of-general-third-order-ordinary-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10010422/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10010422/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10010422/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10010422/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10010422/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10010422/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10010422/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10010422/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10010422/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10010422/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10010422.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">659</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1825</span> Stepsize Control of the Finite Difference Method for Solving Ordinary Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Davod%20Khojasteh%20Salkuyeh">Davod Khojasteh Salkuyeh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>An important task in solving second order linear ordinary differential equations by the finite difference is to choose a suitable stepsize h. In this paper, by using the stochastic arithmetic, the CESTAC method and the CADNA library we present a procedure to estimate the optimal stepsize hopt, the stepsize which minimizes the global error consisting of truncation and round-off error.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Ordinary%20differential%20equations" title="Ordinary differential equations">Ordinary differential equations</a>, <a href="https://publications.waset.org/search?q=optimal%20stepsize" title=" optimal stepsize"> optimal stepsize</a>, <a href="https://publications.waset.org/search?q=error" title=" error"> error</a>, <a href="https://publications.waset.org/search?q=stochastic%20arithmetic" title=" stochastic arithmetic"> stochastic arithmetic</a>, <a href="https://publications.waset.org/search?q=CESTAC" title=" CESTAC"> CESTAC</a>, <a href="https://publications.waset.org/search?q=CADNA." title=" CADNA."> CADNA.</a> </p> <a href="https://publications.waset.org/11434/stepsize-control-of-the-finite-difference-method-for-solving-ordinary-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/11434/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/11434/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/11434/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/11434/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/11434/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/11434/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/11434/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/11434/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/11434/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/11434/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/11434.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1364</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1824</span> Development of Extended Trapezoidal Method for Numerical Solution of Volterra Integro-Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Fuziyah%20Ishak">Fuziyah Ishak</a>, <a href="https://publications.waset.org/search?q=Siti%20Norazura%20Ahmad"> Siti Norazura Ahmad</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>Volterra integro-differential equations appear in many models for real life phenomena. Since analytical solutions for this type of differential equations are hard and at times impossible to attain, engineers and scientists resort to numerical solutions that can be made as accurately as possible. Conventionally, numerical methods for ordinary differential equations are adapted to solve Volterra integro-differential equations. In this paper, numerical solution for solving Volterra integro-differential equation using extended trapezoidal method is described. Formulae for the integral and differential parts of the equation are presented. Numerical results show that the extended method is suitable for solving first order Volterra integro-differential equations.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Accuracy" title="Accuracy">Accuracy</a>, <a href="https://publications.waset.org/search?q=extended%20trapezoidal%20method" title=" extended trapezoidal method"> extended trapezoidal method</a>, <a href="https://publications.waset.org/search?q=numerical%20solution" title=" numerical solution"> numerical solution</a>, <a href="https://publications.waset.org/search?q=Volterra%20integro-differential%20equations." title=" Volterra integro-differential equations. "> Volterra integro-differential equations. </a> </p> <a href="https://publications.waset.org/10005777/development-of-extended-trapezoidal-method-for-numerical-solution-of-volterra-integro-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10005777/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10005777/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10005777/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10005777/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10005777/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10005777/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10005777/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10005777/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10005777/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10005777/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10005777.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1656</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1823</span> Development Partitioning Intervalwise Block Method for Solving Ordinary Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=K.H.Khairul%20Anuar">K.H.Khairul Anuar</a>, <a href="https://publications.waset.org/search?q=K.I.Othman"> K.I.Othman</a>, <a href="https://publications.waset.org/search?q=F.Ishak"> F.Ishak</a>, <a href="https://publications.waset.org/search?q=Z.B.Ibrahim"> Z.B.Ibrahim</a>, <a href="https://publications.waset.org/search?q=Z.Majid"> Z.Majid</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Solving Ordinary Differential Equations (ODEs) by using Partitioning Block Intervalwise (PBI) technique is our aim in this paper. The PBI technique is based on Block Adams Method and Backward Differentiation Formula (BDF). Block Adams Method only use the simple iteration for solving while BDF requires Newtonlike iteration involving Jacobian matrix of ODEs which consumes a considerable amount of computational effort. Therefore, PBI is developed in order to reduce the cost of iteration within acceptable maximum error <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Adam%20Block%20Method" title="Adam Block Method">Adam Block Method</a>, <a href="https://publications.waset.org/search?q=BDF" title=" BDF"> BDF</a>, <a href="https://publications.waset.org/search?q=Ordinary%20Differential%0AEquations" title=" Ordinary Differential Equations"> Ordinary Differential Equations</a>, <a href="https://publications.waset.org/search?q=Partitioning%20Block%20Intervalwise" title=" Partitioning Block Intervalwise"> Partitioning Block Intervalwise</a> </p> <a href="https://publications.waset.org/11574/development-partitioning-intervalwise-block-method-for-solving-ordinary-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/11574/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/11574/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/11574/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/11574/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/11574/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/11574/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/11574/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/11574/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/11574/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/11574/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/11574.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1670</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1822</span> An Accurate Computation of Block Hybrid Method for Solving Stiff Ordinary Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=A.%20M.%20Sagir">A. M. Sagir</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, self-starting block hybrid method of order (5,5,5,5)T is proposed for the solution of the special second order ordinary differential equations with associated initial or boundary conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. The computational burden and computer time wastage involved in the usual reduction of second order problem into system of first order equations are avoided by this approach. Furthermore, a stability analysis and efficiency of the block method are tested on stiff ordinary differential equations, and the results obtained compared favorably with the exact solution. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Block%20Method" title="Block Method">Block Method</a>, <a href="https://publications.waset.org/search?q=Hybrid" title=" Hybrid"> Hybrid</a>, <a href="https://publications.waset.org/search?q=Linear%20Multistep%20Method" title=" Linear Multistep Method"> Linear Multistep Method</a>, <a href="https://publications.waset.org/search?q=Self%0A%E2%80%93%20starting" title=" Self – starting"> Self – starting</a>, <a href="https://publications.waset.org/search?q=Special%20Second%20Order." title=" Special Second Order."> Special Second Order.</a> </p> <a href="https://publications.waset.org/15640/an-accurate-computation-of-block-hybrid-method-for-solving-stiff-ordinary-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/15640/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/15640/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/15640/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/15640/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/15640/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/15640/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/15640/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/15640/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/15640/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/15640/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/15640.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1481</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1821</span> Laplace Technique to Find General Solution of Differential Equations without Initial Conditions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Adil%20Al-Rammahi">Adil Al-Rammahi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>Laplace transformations have wide applications in engineering and sciences. All previous studies of modified Laplace transformations depend on differential equation with initial conditions. The purpose of our paper is to solve the linear differential equations (not initial value problem) and then find the general solution (not particular) via the Laplace transformations without needed any initial condition. The study involves both types of differential equations, ordinary and partial.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Differential%20Equations" title="Differential Equations">Differential Equations</a>, <a href="https://publications.waset.org/search?q=Laplace%20Transformations." title=" Laplace Transformations."> Laplace Transformations.</a> </p> <a href="https://publications.waset.org/10000213/laplace-technique-to-find-general-solution-of-differential-equations-without-initial-conditions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10000213/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10000213/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10000213/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10000213/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10000213/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10000213/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10000213/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10000213/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10000213/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10000213/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10000213.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">3184</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1820</span> On a New Inverse Polynomial Numerical Scheme for the Solution of Initial Value Problems in Ordinary Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=R.%20B.%20Ogunrinde">R. B. Ogunrinde</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents the development, analysis and implementation of an inverse polynomial numerical method which is well suitable for solving initial value problems in first order ordinary differential equations with applications to sample problems. We also present some basic concepts and fundamental theories which are vital to the analysis of the scheme. We analyzed the consistency, convergence, and stability properties of the scheme. Numerical experiments were carried out and the results compared with the theoretical or exact solution and the algorithm was later coded using MATLAB programming language. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Differential%20equations" title="Differential equations">Differential equations</a>, <a href="https://publications.waset.org/search?q=Numerical" title=" Numerical"> Numerical</a>, <a href="https://publications.waset.org/search?q=Initial%20value%0D%0Aproblem" title=" Initial value problem"> Initial value problem</a>, <a href="https://publications.waset.org/search?q=Polynomials." title=" Polynomials."> Polynomials.</a> </p> <a href="https://publications.waset.org/10002157/on-a-new-inverse-polynomial-numerical-scheme-for-the-solution-of-initial-value-problems-in-ordinary-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10002157/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10002157/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10002157/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10002157/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10002157/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10002157/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10002157/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10002157/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10002157/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10002157/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10002157.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1772</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1819</span> A Family of Zero Stable Block Integrator for the Solutions of Ordinary Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=A.%20M.%20Sagir">A. M. Sagir</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, linear multistep technique using power series as the basis function is used to develop the block methods which are suitable for generating direct solution of the special second order ordinary differential equations with associated initial or boundary conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain two different four discrete schemes, each of order (5,5,5,5)T, which were used in block form for parallel or sequential solutions of the problems. The computational burden and computer time wastage involved in the usual reduction of second order problem into system of first order equations are avoided by this approach. Furthermore, a stability analysis and efficiency of the block methods are tested on linear and non-linear ordinary differential equations and the results obtained compared favorably with the exact solution. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Block%20Method" title="Block Method">Block Method</a>, <a href="https://publications.waset.org/search?q=Hybrid" title=" Hybrid"> Hybrid</a>, <a href="https://publications.waset.org/search?q=Linear%20Multistep%20Method" title=" Linear Multistep Method"> Linear Multistep Method</a>, <a href="https://publications.waset.org/search?q=Self%20%E2%80%93%20starting" title=" Self – starting"> Self – starting</a>, <a href="https://publications.waset.org/search?q=Special%20Second%20Order." title=" Special Second Order."> Special Second Order.</a> </p> <a href="https://publications.waset.org/10892/a-family-of-zero-stable-block-integrator-for-the-solutions-of-ordinary-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10892/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10892/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10892/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10892/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10892/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10892/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10892/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10892/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10892/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10892/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10892.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1483</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1818</span> 2 – Block 3 - Point Modified Numerov Block Methods for Solving Ordinary Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Abdu%20Masanawa%20Sagir">Abdu Masanawa Sagir</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, linear multistep technique using power series as the basis function is used to develop the block methods which are suitable for generating direct solution of the special second order ordinary differential equations of the form y′′ = f(x,y), a < = x < = b with associated initial or boundary conditions. The continuaous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain two different three discrete schemes, each of order (4,4,4)T, which were used in block form for parallel or sequential solutions of the problems. The computational burden and computer time wastage involved in the usual reduction of second order problem into system of first order equations are avoided by this approach. Furthermore, a stability analysis and efficiency of the block method are tested on linear and non-linear ordinary differential equations whose solutions are oscillatory or nearly periodic in nature, and the results obtained compared favourably with the exact solution. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Block%20Method" title="Block Method">Block Method</a>, <a href="https://publications.waset.org/search?q=Hybrid" title=" Hybrid"> Hybrid</a>, <a href="https://publications.waset.org/search?q=Linear%20Multistep%20Method" title=" Linear Multistep Method"> Linear Multistep Method</a>, <a href="https://publications.waset.org/search?q=Self%20%E2%80%93%20starting" title=" Self – starting"> Self – starting</a>, <a href="https://publications.waset.org/search?q=Special%20Second%20Order." title=" Special Second Order."> Special Second Order.</a> </p> <a href="https://publications.waset.org/3752/2-block-3-point-modified-numerov-block-methods-for-solving-ordinary-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/3752/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/3752/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/3752/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/3752/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/3752/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/3752/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/3752/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/3752/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/3752/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/3752/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/3752.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1950</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1817</span> Numerical Solution of Second-Order Ordinary Differential Equations by Improved Runge-Kutta Nystrom Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Faranak%20Rabiei">Faranak Rabiei</a>, <a href="https://publications.waset.org/search?q=Fudziah%20Ismail"> Fudziah Ismail</a>, <a href="https://publications.waset.org/search?q=S.%20Norazak"> S. Norazak</a>, <a href="https://publications.waset.org/search?q=Saeid%20Emadi"> Saeid Emadi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper we developed the Improved Runge-Kutta Nystrom (IRKN) method for solving second order ordinary differential equations. The methods are two step in nature and require lower number of function evaluations per step compared with the existing Runge-Kutta Nystrom (RKN) methods. Therefore, the methods are computationally more efficient at achieving the higher order of local accuracy. Algebraic order conditions of the method are obtained and the third and fourth order method are derived with two and three stages respectively. The numerical results are given to illustrate the efficiency of the proposed method compared to the existing RKN methods.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Improved%20Runge-Kutta%20Nystrom%20method" title="Improved Runge-Kutta Nystrom method">Improved Runge-Kutta Nystrom method</a>, <a href="https://publications.waset.org/search?q=Two%20step%20method" title=" Two step method"> Two step method</a>, <a href="https://publications.waset.org/search?q=Second-order%20ordinary%20differential%20equations" title=" Second-order ordinary differential equations"> Second-order ordinary differential equations</a>, <a href="https://publications.waset.org/search?q=Order%20conditions" title=" Order conditions"> Order conditions</a> </p> <a href="https://publications.waset.org/1175/numerical-solution-of-second-order-ordinary-differential-equations-by-improved-runge-kutta-nystrom-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/1175/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/1175/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/1175/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/1175/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/1175/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/1175/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/1175/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/1175/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/1175/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/1175/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/1175.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">6850</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1816</span> The Origin, Diffusion and a Comparison of Ordinary Differential Equations Numerical Solutions Used by SIR Model in Order to Predict SARS-CoV-2 in Nordic Countries</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Gleda%20Kutrolli">Gleda Kutrolli</a>, <a href="https://publications.waset.org/search?q=Maksi%20Kutrolli"> Maksi Kutrolli</a>, <a href="https://publications.waset.org/search?q=Etjon%20Meco"> Etjon Meco</a> </p> <p class="card-text"><strong>Abstract:</strong></p> SARS-CoV-2 virus is currently one of the most infectious pathogens for humans. It started in China at the end of 2019 and now it is spread in all over the world. The origin and diffusion of the SARS-CoV-2 epidemic, is analysed based on the discussion of viral phylogeny theory. With the aim of understanding the spread of infection in the affected countries, it is crucial to modelize the spread of the virus and simulate its activity. In this paper, the prediction of coronavirus outbreak is done by using SIR model without vital dynamics, applying different numerical technique solving ordinary differential equations (ODEs). We find out that ABM and MRT methods perform better than other techniques and that the activity of the virus will decrease in April but it never cease (for some time the activity will remain low) and the next cycle will start in the middle July 2020 for Norway and Denmark, and October 2020 for Sweden, and September for Finland. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Forecasting" title="Forecasting">Forecasting</a>, <a href="https://publications.waset.org/search?q=ordinary%20differential%20equations" title=" ordinary differential equations"> ordinary differential equations</a>, <a href="https://publications.waset.org/search?q=SARS-CoV-2%20epidemic" title=" SARS-CoV-2 epidemic"> SARS-CoV-2 epidemic</a>, <a href="https://publications.waset.org/search?q=SIR%20model." title=" SIR model."> SIR model.</a> </p> <a href="https://publications.waset.org/10011742/the-origin-diffusion-and-a-comparison-of-ordinary-differential-equations-numerical-solutions-used-by-sir-model-in-order-to-predict-sars-cov-2-in-nordic-countries" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10011742/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10011742/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10011742/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10011742/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10011742/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10011742/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10011742/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10011742/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10011742/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10011742/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10011742.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">558</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1815</span> Parallel Block Backward Differentiation Formulas for Solving Ordinary Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Khairil%20Iskandar%20Othman">Khairil Iskandar Othman</a>, <a href="https://publications.waset.org/search?q=Zarina%20Bibi%20Ibrahim"> Zarina Bibi Ibrahim</a>, <a href="https://publications.waset.org/search?q=Mohamed%20Suleiman"> Mohamed Suleiman</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A parallel block method based on Backward Differentiation Formulas (BDF) is developed for the parallel solution of stiff Ordinary Differential Equations (ODEs). Most common methods for solving stiff systems of ODEs are based on implicit formulae and solved using Newton iteration which requires repeated solution of systems of linear equations with coefficient matrix, I - hβJ . Here, J is the Jacobian matrix of the problem. In this paper, the matrix operations is paralleled in order to reduce the cost of the iterations. Numerical results are given to compare the speedup and efficiency of parallel algorithm and that of sequential algorithm. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Backward%20Differentiation%20Formula" title="Backward Differentiation Formula">Backward Differentiation Formula</a>, <a href="https://publications.waset.org/search?q=block" title=" block"> block</a>, <a href="https://publications.waset.org/search?q=ordinarydifferential%20equations." title=" ordinarydifferential equations."> ordinarydifferential equations.</a> </p> <a href="https://publications.waset.org/7693/parallel-block-backward-differentiation-formulas-for-solving-ordinary-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/7693/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/7693/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/7693/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/7693/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/7693/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/7693/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/7693/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/7693/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/7693/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/7693/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/7693.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">2011</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1814</span> Ordinary Differential Equations with Inverted Functions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Thomas%20Kampke">Thomas Kampke</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>Equations with differentials relating to the inverse of an unknown function rather than to the unknown function itself are solved exactly for some special cases and numerically for the general case. Invertibility combined with differentiability over connected domains forces solutions always to be monotone. Numerical function inversion is key to all solution algorithms which either are of a forward type or a fixed point type considering whole approximate solution functions in each iteration. The given considerations are restricted to ordinary differential equations with inverted functions (ODEIs) of first order. Forward type computations, if applicable, admit consistency of order one and, under an additional accuracy condition, convergence of order one.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Euler%20method" title="Euler method">Euler method</a>, <a href="https://publications.waset.org/search?q=fixed%20points" title=" fixed points"> fixed points</a>, <a href="https://publications.waset.org/search?q=golden%20section" title=" golden section"> golden section</a>, <a href="https://publications.waset.org/search?q=multi-step%20procedures" title=" multi-step procedures"> multi-step procedures</a>, <a href="https://publications.waset.org/search?q=Runge%20Kutta%20methods." title=" Runge Kutta methods."> Runge Kutta methods.</a> </p> <a href="https://publications.waset.org/4337/ordinary-differential-equations-with-inverted-functions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/4337/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/4337/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/4337/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/4337/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/4337/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/4337/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/4337/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/4337/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/4337/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/4337/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/4337.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1448</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1813</span> Evolutionary Computing Approach for the Solution of Initial value Problems in Ordinary Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=A.%20Junaid">A. Junaid</a>, <a href="https://publications.waset.org/search?q=M.%20A.%20Z.%20Raja"> M. A. Z. Raja</a>, <a href="https://publications.waset.org/search?q=I.%20M.%20Qureshi"> I. M. Qureshi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>An evolutionary computing technique for solving initial value problems in Ordinary Differential Equations is proposed in this paper. Neural network is used as a universal approximator while the adaptive parameters of neural networks are optimized by genetic algorithm. The solution is achieved on the continuous grid of time instead of discrete as in other numerical techniques. The comparison is carried out with classical numerical techniques and the solution is found with a uniform accuracy of MSE ≈ 10-9 .</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Neural%20networks" title="Neural networks">Neural networks</a>, <a href="https://publications.waset.org/search?q=Unsupervised%20learning" title=" Unsupervised learning"> Unsupervised learning</a>, <a href="https://publications.waset.org/search?q=Evolutionary%20computing" title=" Evolutionary computing"> Evolutionary computing</a>, <a href="https://publications.waset.org/search?q=Numerical%20methods" title=" Numerical methods"> Numerical methods</a>, <a href="https://publications.waset.org/search?q=Fitness%20evaluation%0D%0Afunction." title=" Fitness evaluation function."> Fitness evaluation function.</a> </p> <a href="https://publications.waset.org/12849/evolutionary-computing-approach-for-the-solution-of-initial-value-problems-in-ordinary-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/12849/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/12849/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/12849/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/12849/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/12849/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/12849/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/12849/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/12849/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/12849/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/12849/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/12849.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1780</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1812</span> Application of the Hybrid Methods to Solving Volterra Integro-Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=G.Mehdiyeva">G.Mehdiyeva</a>, <a href="https://publications.waset.org/search?q=M.Imanova"> M.Imanova</a>, <a href="https://publications.waset.org/search?q=V.Ibrahimov"> V.Ibrahimov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Beginning from the creator of integro-differential equations Volterra, many scientists have investigated these equations. Classic method for solving integro-differential equations is the quadratures method that is successfully applied up today. Unlike these methods, Makroglou applied hybrid methods that are modified and generalized in this paper and applied to the numerical solution of Volterra integro-differential equations. The way for defining the coefficients of the suggested method is also given. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Integro-differential%20equations" title="Integro-differential equations">Integro-differential equations</a>, <a href="https://publications.waset.org/search?q=initial%20value%0Aproblem" title=" initial value problem"> initial value problem</a>, <a href="https://publications.waset.org/search?q=hybrid%20methods" title=" hybrid methods"> hybrid methods</a>, <a href="https://publications.waset.org/search?q=predictor-corrector%20method" title=" predictor-corrector method"> predictor-corrector method</a> </p> <a href="https://publications.waset.org/11196/application-of-the-hybrid-methods-to-solving-volterra-integro-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/11196/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/11196/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/11196/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/11196/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/11196/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/11196/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/11196/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/11196/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/11196/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/11196/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/11196.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1732</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1811</span> On Problem of Parameters Identification of Dynamic Object</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Kamil%20Aida-zade">Kamil Aida-zade</a>, <a href="https://publications.waset.org/search?q=C.%20Ardil"> C. Ardil</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, some problem formulations of dynamic object parameters recovery described by non-autonomous system of ordinary differential equations with multipoint unshared edge conditions are investigated. Depending on the number of additional conditions the problem is reduced to an algebraic equations system or to a problem of quadratic programming. With this purpose the paper offers a new scheme of the edge conditions transfer method called by conditions shift. The method permits to get rid from differential links and multipoint unshared initially-edge conditions. The advantage of the proposed approach is concluded by capabilities of reduction of a parametric identification problem to essential simple problems of the solution of an algebraic system or quadratic programming. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=dynamic%20objects" title="dynamic objects">dynamic objects</a>, <a href="https://publications.waset.org/search?q=ordinary%20differential%20equations" title=" ordinary differential equations"> ordinary differential equations</a>, <a href="https://publications.waset.org/search?q=multipoint%20unshared%20edge%20conditions" title="multipoint unshared edge conditions">multipoint unshared edge conditions</a>, <a href="https://publications.waset.org/search?q=quadratic%20programming" title=" quadratic programming"> quadratic programming</a>, <a href="https://publications.waset.org/search?q=conditions%20shift" title="conditions shift">conditions shift</a> </p> <a href="https://publications.waset.org/6135/on-problem-of-parameters-identification-of-dynamic-object" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/6135/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/6135/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/6135/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/6135/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/6135/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/6135/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/6135/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/6135/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/6135/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/6135/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/6135.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1457</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1810</span> Strict Stability of Fuzzy Differential Equations by Lyapunov Functions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Mustafa%20Bayram%20G%C3%BCcen">Mustafa Bayram Gücen</a>, <a href="https://publications.waset.org/search?q=Co%C5%9Fkun%20Yakar"> Coşkun Yakar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this study, we have investigated the strict stability of fuzzy differential systems and we compare the classical notion of strict stability criteria of ordinary differential equations and the notion of strict stability of fuzzy differential systems. In addition that, we present definitions of stability and strict stability of fuzzy differential equations and also we have some theorems and comparison results. Strict Stability is a different stability definition and this stability type can give us an information about the rate of decay of the solutions. Lyapunov’s second method is a standard technique used in the study of the qualitative behavior of fuzzy differential systems along with a comparison result that allows the prediction of behavior of a fuzzy differential system when the behavior of the null solution of a fuzzy comparison system is known. This method is a usefull for investigating strict stability of fuzzy systems. First of all, we present definitions and necessary background material. Secondly, we discuss and compare the differences between the classical notion of stability and the recent notion of strict stability. And then, we have a comparison result in which the stability properties of the null solution of the comparison system imply the corresponding stability properties of the fuzzy differential system. Consequently, we give the strict stability results and a comparison theorem. We have used Lyapunov second method and we have proved a comparison result with scalar differential equations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Fuzzy%20systems" title="Fuzzy systems">Fuzzy systems</a>, <a href="https://publications.waset.org/search?q=fuzzy%20differential%20equations" title=" fuzzy differential equations"> fuzzy differential equations</a>, <a href="https://publications.waset.org/search?q=fuzzy%0D%0Astability" title=" fuzzy stability"> fuzzy stability</a>, <a href="https://publications.waset.org/search?q=strict%20stability." title=" strict stability."> strict stability.</a> </p> <a href="https://publications.waset.org/10009010/strict-stability-of-fuzzy-differential-equations-by-lyapunov-functions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10009010/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10009010/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10009010/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10009010/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10009010/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10009010/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10009010/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10009010/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10009010/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10009010/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10009010.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1127</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1809</span> Step Method for Solving Nonlinear Two Delays Differential Equation in Parkinson’s Disease</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=H.%20N.%20Agiza">H. N. Agiza</a>, <a href="https://publications.waset.org/search?q=M.%20A.%20Sohaly"> M. A. Sohaly</a>, <a href="https://publications.waset.org/search?q=M.%20A.%20Elfouly"> M. A. Elfouly</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>Parkinson's disease (PD) is a heterogeneous disorder with common age of onset, symptoms, and progression levels. In this paper we will solve analytically the PD model as a non-linear delay differential equation using the steps method. The step method transforms a system of delay differential equations (DDEs) into systems of ordinary differential equations (ODEs). On some numerical examples, the analytical solution will be difficult. So we will approximate the analytical solution using Picard method and Taylor method to ODEs<em>.</em></p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Parkinson%27s%20disease" title="Parkinson's disease">Parkinson's disease</a>, <a href="https://publications.waset.org/search?q=Step%20method" title=" Step method"> Step method</a>, <a href="https://publications.waset.org/search?q=delay%20differential%20equation" title=" delay differential equation"> delay differential equation</a>, <a href="https://publications.waset.org/search?q=simulation." title=" simulation."> simulation.</a> </p> <a href="https://publications.waset.org/10011637/step-method-for-solving-nonlinear-two-delays-differential-equation-in-parkinsons-disease" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10011637/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10011637/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10011637/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10011637/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10011637/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10011637/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10011637/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10011637/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10011637/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10011637/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10011637.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">733</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1808</span> The RK1GL2X3 Method for Initial Value Problems in Ordinary Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=J.S.C.%20Prentice">J.S.C. Prentice</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>The RK1GL2X3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on the RK1GL2 method which, in turn, is a particular case of the general RKrGLm method. The RK1GL2X3 method is a fourth-order method, even though its underlying Runge-Kutta method RK1 is the first-order Euler method, and hence, RK1GL2X3 is considerably more efficient than RK1. This enhancement is achieved through an implementation involving triple-nested two-point Gauss- Legendre quadrature.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=RK1GL2X3" title="RK1GL2X3">RK1GL2X3</a>, <a href="https://publications.waset.org/search?q=RK1GL2" title=" RK1GL2"> RK1GL2</a>, <a href="https://publications.waset.org/search?q=RKrGLm" title=" RKrGLm"> RKrGLm</a>, <a href="https://publications.waset.org/search?q=Runge-Kutta" title=" Runge-Kutta"> Runge-Kutta</a>, <a href="https://publications.waset.org/search?q=Gauss-Legendre" title=" Gauss-Legendre"> Gauss-Legendre</a>, <a href="https://publications.waset.org/search?q=initial%20value%20problem" title=" initial value problem"> initial value problem</a>, <a href="https://publications.waset.org/search?q=local%20error" title=" local error"> local error</a>, <a href="https://publications.waset.org/search?q=global%20error." title=" global error."> global error.</a> </p> <a href="https://publications.waset.org/8881/the-rk1gl2x3-method-for-initial-value-problems-in-ordinary-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/8881/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/8881/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/8881/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/8881/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/8881/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/8881/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/8881/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/8881/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/8881/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/8881/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/8881.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1318</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1807</span> Direct Block Backward Differentiation Formulas for Solving Second Order Ordinary Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Zarina%20Bibi%20Ibrahim">Zarina Bibi Ibrahim</a>, <a href="https://publications.waset.org/search?q=Mohamed%20Suleiman"> Mohamed Suleiman</a>, <a href="https://publications.waset.org/search?q=Khairil%20Iskandar%20Othman"> Khairil Iskandar Othman</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, a direct method based on variable step size Block Backward Differentiation Formula which is referred as BBDF2 for solving second order Ordinary Differential Equations (ODEs) is developed. The advantages of the BBDF2 method over the corresponding sequential variable step variable order Backward Differentiation Formula (BDFVS) when used to solve the same problem as a first order system are pointed out. Numerical results are given to validate the method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Backward%20Differentiation%20Formula" title="Backward Differentiation Formula">Backward Differentiation Formula</a>, <a href="https://publications.waset.org/search?q=block" title=" block"> block</a>, <a href="https://publications.waset.org/search?q=secondorder." title=" secondorder."> secondorder.</a> </p> <a href="https://publications.waset.org/7863/direct-block-backward-differentiation-formulas-for-solving-second-order-ordinary-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/7863/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/7863/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/7863/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/7863/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/7863/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/7863/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/7863/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/7863/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/7863/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/7863/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/7863.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">2026</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1806</span> The Global Stability Using Lyapunov Function</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=R.%20Kongnuy">R. Kongnuy</a>, <a href="https://publications.waset.org/search?q=E.%20Naowanich"> E. Naowanich</a>, <a href="https://publications.waset.org/search?q=T.%20Kruehong"> T. Kruehong</a> </p> <p class="card-text"><strong>Abstract:</strong></p> An important technique in stability theory for differential equations is known as the direct method of Lyapunov. In this work we deal global stability properties of Leptospirosis transmission model by age group in Thailand. First we consider the data from Division of Epidemiology Ministry of Public Health, Thailand between 1997-2011. Then we construct the mathematical model for leptospirosis transmission by eight age groups. The Lyapunov functions are used for our model which takes the forms of an Ordinary Differential Equation system. The globally asymptotically for equilibrium states are analyzed. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Age%20Group" title="Age Group">Age Group</a>, <a href="https://publications.waset.org/search?q=Leptospirosis" title=" Leptospirosis"> Leptospirosis</a>, <a href="https://publications.waset.org/search?q=Lyapunov%20Function" title=" Lyapunov Function"> Lyapunov Function</a>, <a href="https://publications.waset.org/search?q=Ordinary%20Differential%20Equation." title=" Ordinary Differential Equation."> Ordinary Differential Equation.</a> </p> <a href="https://publications.waset.org/15304/the-global-stability-using-lyapunov-function" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/15304/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/15304/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/15304/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/15304/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/15304/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/15304/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/15304/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/15304/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/15304/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/15304/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/15304.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">2148</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1805</span> Constructing Distinct Kinds of Solutions for the Time-Dependent Coefficients Coupled Klein-Gordon-Schrödinger Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Anupma%20Bansal">Anupma Bansal</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>We seek exact solutions of the coupled Klein-Gordon-Schrödinger equation with variable coefficients with the aid of Lie classical approach. By using the Lie classical method, we are able to derive symmetries that are used for reducing the coupled system of partial differential equations into ordinary differential equations. From reduced differential equations we have derived some new exact solutions of coupled Klein-Gordon-Schrödinger equations involving some special functions such as Airy wave functions, Bessel functions, Mathieu functions etc.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Klein-Gordon-Sch%C3%B6dinger%20Equation" title="Klein-Gordon-Schödinger Equation">Klein-Gordon-Schödinger Equation</a>, <a href="https://publications.waset.org/search?q=Lie%20Classical%20Method" title=" Lie Classical Method"> Lie Classical Method</a>, <a href="https://publications.waset.org/search?q=Exact%20Solutions" title=" Exact Solutions"> Exact Solutions</a> </p> <a href="https://publications.waset.org/16742/constructing-distinct-kinds-of-solutions-for-the-time-dependent-coefficients-coupled-klein-gordon-schrodinger-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/16742/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/16742/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/16742/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/16742/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/16742/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/16742/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/16742/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/16742/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/16742/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/16742/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/16742.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">4530</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1804</span> Blow up in Polynomial Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Rudolf%20Csikja">Rudolf Csikja</a>, <a href="https://publications.waset.org/search?q=Janos%20Toth"> Janos Toth</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>Methods to detect and localize time singularities of polynomial and quasi-polynomial ordinary differential equations are systematically presented and developed. They are applied to examples taken form different fields of applications and they are also compared to better known methods such as those based on the existence of linear first integrals or Lyapunov functions.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=blow%20up" title="blow up">blow up</a>, <a href="https://publications.waset.org/search?q=finite%20escape%20time" title=" finite escape time"> finite escape time</a>, <a href="https://publications.waset.org/search?q=polynomial%20ODE" title=" polynomial ODE"> polynomial ODE</a>, <a href="https://publications.waset.org/search?q=singularity" title=" singularity"> singularity</a>, <a href="https://publications.waset.org/search?q=Lotka%E2%80%93Volterra%20equation" title=" Lotka–Volterra equation"> Lotka–Volterra equation</a>, <a href="https://publications.waset.org/search?q=Painleve%20analysis" title=" Painleve analysis"> Painleve analysis</a>, <a href="https://publications.waset.org/search?q=%CE%A8-series" title=" Ψ-series"> Ψ-series</a>, <a href="https://publications.waset.org/search?q=global%20existence" title=" global existence"> global existence</a> </p> <a href="https://publications.waset.org/7512/blow-up-in-polynomial-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/7512/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/7512/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/7512/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/7512/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/7512/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/7512/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/7512/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/7512/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/7512/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/7512/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/7512.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">2182</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1803</span> A First Course in Numerical Methods with “Mathematica“</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Andrei%20A.%20Kolyshkin">Andrei A. Kolyshkin</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In the present paper some recommendations for the use of software package “Mathematica" in a basic numerical analysis course are presented. The methods which are covered in the course include solution of systems of linear equations, nonlinear equations and systems of nonlinear equations, numerical integration, interpolation and solution of ordinary differential equations. A set of individual assignments developed for the course covering all the topics is discussed in detail. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Numerical%20methods" title="Numerical methods">Numerical methods</a>, <a href="https://publications.waset.org/search?q=%22Mathematica%22" title=" "Mathematica""> "Mathematica"</a>, <a href="https://publications.waset.org/search?q=e-learning." title=" e-learning."> e-learning.</a> </p> <a href="https://publications.waset.org/2466/a-first-course-in-numerical-methods-with-mathematica" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/2466/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/2466/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/2466/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/2466/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/2466/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/2466/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/2466/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/2466/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/2466/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/2466/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/2466.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">3670</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1802</span> Numerical Investigation of Two-dimensional Boundary Layer Flow Over a Moving Surface</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Mahmoud%20Zarrini">Mahmoud Zarrini</a>, <a href="https://publications.waset.org/search?q=R.N.%20Pralhad"> R.N. Pralhad</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this chapter, we have studied Variation of velocity in incompressible fluid over a moving surface. The boundary layer equations are on a fixed or continuously moving flat plate in the same or opposite direction to the free stream with suction and injection. The boundary layer equations are transferred from partial differential equations to ordinary differential equations. Numerical solutions are obtained by using Runge-Kutta and Shooting methods. We have found numerical solution to velocity and skin friction coefficient.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Boundary%20layer" title="Boundary layer">Boundary layer</a>, <a href="https://publications.waset.org/search?q=continuously%20moving%20surface" title=" continuously moving surface"> continuously moving surface</a>, <a href="https://publications.waset.org/search?q=shooting%20method" title=" shooting method"> shooting method</a>, <a href="https://publications.waset.org/search?q=skin%20friction%20coefficient." title=" skin friction coefficient."> skin friction coefficient.</a> </p> <a href="https://publications.waset.org/15641/numerical-investigation-of-two-dimensional-boundary-layer-flow-over-a-moving-surface" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/15641/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/15641/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/15641/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/15641/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/15641/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/15641/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/15641/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/15641/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/15641/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/15641/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/15641.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1576</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1801</span> Implicit Two Step Continuous Hybrid Block Methods with Four Off-Steps Points for Solving Stiff Ordinary Differential Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=O.%20A.%20Akinfenwa">O. A. Akinfenwa</a>, <a href="https://publications.waset.org/search?q=N.M.%20Yao"> N.M. Yao</a>, <a href="https://publications.waset.org/search?q=S.%20N.%20Jator"> S. N. Jator</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, a self starting two step continuous block hybrid formulae (CBHF) with four Off-step points is developed using collocation and interpolation procedures. The CBHF is then used to produce multiple numerical integrators which are of uniform order and are assembled into a single block matrix equation. These equations are simultaneously applied to provide the approximate solution for the stiff ordinary differential equations. The order of accuracy and stability of the block method is discussed and its accuracy is established numerically. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Collocation%20and%20Interpolation" title="Collocation and Interpolation">Collocation and Interpolation</a>, <a href="https://publications.waset.org/search?q=Continuous%20HybridBlock%20Formulae" title=" Continuous HybridBlock Formulae"> Continuous HybridBlock Formulae</a>, <a href="https://publications.waset.org/search?q=Off-Step%20Points" title=" Off-Step Points"> Off-Step Points</a>, <a href="https://publications.waset.org/search?q=Stability" title=" Stability"> Stability</a>, <a href="https://publications.waset.org/search?q=Stiff%20ODEs." title=" Stiff ODEs."> Stiff ODEs.</a> </p> <a href="https://publications.waset.org/8824/implicit-two-step-continuous-hybrid-block-methods-with-four-off-steps-points-for-solving-stiff-ordinary-differential-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/8824/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/8824/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/8824/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/8824/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/8824/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/8824/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/8824/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/8824/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/8824/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/8824/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/8824.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">2098</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1800</span> On Symmetries and Exact Solutions of Einstein Vacuum Equations for Axially Symmetric Gravitational Fields</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Nisha%20Goyal">Nisha Goyal</a>, <a href="https://publications.waset.org/search?q=R.K.%20Gupta"> R.K. Gupta</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Einstein vacuum equations, that is a system of nonlinear partial differential equations (PDEs) are derived from Weyl metric by using relation between Einstein tensor and metric tensor. The symmetries of Einstein vacuum equations for static axisymmetric gravitational fields are obtained using the Lie classical method. We have examined the optimal system of vector fields which is further used to reduce nonlinear PDE to nonlinear ordinary differential equation (ODE). Some exact solutions of Einstein vacuum equations in general relativity are also obtained. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Gravitational%20fields" title="Gravitational fields">Gravitational fields</a>, <a href="https://publications.waset.org/search?q=Lie%20Classical%20method" title=" Lie Classical method"> Lie Classical method</a>, <a href="https://publications.waset.org/search?q=Exact%20solutions." title=" Exact solutions."> Exact solutions.</a> </p> <a href="https://publications.waset.org/14108/on-symmetries-and-exact-solutions-of-einstein-vacuum-equations-for-axially-symmetric-gravitational-fields" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/14108/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/14108/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/14108/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/14108/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/14108/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/14108/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/14108/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/14108/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/14108/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/14108/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/14108.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1934</span> </span> </div> </div> <ul class="pagination"> <li class="page-item disabled"><span class="page-link">&lsaquo;</span></li> <li class="page-item active"><span class="page-link">1</span></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/search?q=Ordinary%20differential%20equations&page=2">2</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/search?q=Ordinary%20differential%20equations&page=3">3</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/search?q=Ordinary%20differential%20equations&page=4">4</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/search?q=Ordinary%20differential%20equations&page=5">5</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/search?q=Ordinary%20differential%20equations&page=6">6</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/search?q=Ordinary%20differential%20equations&page=7">7</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/search?q=Ordinary%20differential%20equations&page=8">8</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/search?q=Ordinary%20differential%20equations&page=9">9</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/search?q=Ordinary%20differential%20equations&page=10">10</a></li> <li class="page-item disabled"><span class="page-link">...</span></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/search?q=Ordinary%20differential%20equations&page=60">60</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/search?q=Ordinary%20differential%20equations&page=61">61</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/search?q=Ordinary%20differential%20equations&page=2" rel="next">&rsaquo;</a></li> </ul> </div> </main> <footer> <div id="infolinks" class="pt-3 pb-2"> <div class="container"> <div style="background-color:#f5f5f5;" class="p-3"> <div class="row"> <div class="col-md-2"> <ul class="list-unstyled"> About <li><a href="https://waset.org/page/support">About Us</a></li> <li><a href="https://waset.org/page/support#legal-information">Legal</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/WASET-16th-foundational-anniversary.pdf">WASET celebrates its 16th foundational anniversary</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Account <li><a href="https://waset.org/profile">My Account</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Explore <li><a href="https://waset.org/disciplines">Disciplines</a></li> <li><a href="https://waset.org/conferences">Conferences</a></li> <li><a href="https://waset.org/conference-programs">Conference Program</a></li> <li><a href="https://waset.org/committees">Committees</a></li> <li><a href="https://publications.waset.org">Publications</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Research <li><a href="https://publications.waset.org/abstracts">Abstracts</a></li> <li><a href="https://publications.waset.org">Periodicals</a></li> <li><a href="https://publications.waset.org/archive">Archive</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Open Science <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Open-Science-Philosophy.pdf">Open Science Philosophy</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Open-Science-Award.pdf">Open Science Award</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Open-Society-Open-Science-and-Open-Innovation.pdf">Open Innovation</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Postdoctoral-Fellowship-Award.pdf">Postdoctoral Fellowship Award</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Scholarly-Research-Review.pdf">Scholarly Research Review</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Support <li><a href="https://waset.org/page/support">Support</a></li> <li><a href="https://waset.org/profile/messages/create">Contact Us</a></li> <li><a href="https://waset.org/profile/messages/create">Report Abuse</a></li> </ul> </div> </div> </div> </div> </div> <div class="container text-center"> <hr style="margin-top:0;margin-bottom:.3rem;"> <a href="https://creativecommons.org/licenses/by/4.0/" target="_blank" class="text-muted small">Creative Commons Attribution 4.0 International License</a> <div id="copy" class="mt-2">© 2024 World Academy of Science, Engineering and Technology</div> </div> </footer> <a href="javascript:" id="return-to-top"><i class="fas fa-arrow-up"></i></a> <div class="modal" id="modal-template"> <div class="modal-dialog"> <div class="modal-content"> <div class="row m-0 mt-1"> <div class="col-md-12"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> </div> </div> <div class="modal-body"></div> </div> </div> </div> <script src="https://cdn.waset.org/static/plugins/jquery-3.3.1.min.js"></script> <script src="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/js/bootstrap.bundle.min.js"></script> <script src="https://cdn.waset.org/static/js/site.js?v=150220211556"></script> <script> jQuery(document).ready(function() { /*jQuery.get("https://publications.waset.org/xhr/user-menu", function (response) { jQuery('#mainNavMenu').append(response); });*/ jQuery.get({ url: "https://publications.waset.org/xhr/user-menu", cache: false }).then(function(response){ jQuery('#mainNavMenu').append(response); }); }); </script> </body> </html>