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ordinary differential equations</title> <meta name="description" content="Search results for: nonlinear ordinary differential equations"> <meta name="keywords" content="nonlinear 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 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nonlinear 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">2634</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">2633</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">2632</span> An Efficient Computational Algorithm for Solving the Nonlinear Lane-Emden Type Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Gholamreza%20Hojjati">Gholamreza Hojjati</a>, <a href="https://publications.waset.org/search?q=Kourosh%20Parand"> Kourosh Parand</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper we propose a class of second derivative multistep methods for solving some well-known classes of Lane- Emden type equations which are nonlinear ordinary differential equations on the semi-infinite domain. These methods, which have good stability and accuracy properties, are useful in deal with stiff ODEs. We show superiority of these methods by applying them on the some famous Lane-Emden type equations.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Lane-Emden%20type%20equations" title="Lane-Emden type equations">Lane-Emden type equations</a>, <a href="https://publications.waset.org/search?q=nonlinear%20ODE" title=" nonlinear ODE"> nonlinear ODE</a>, <a href="https://publications.waset.org/search?q=stiff%20problems" title=" stiff problems"> stiff problems</a>, <a href="https://publications.waset.org/search?q=multistep%20methods" title=" multistep methods"> multistep methods</a>, <a href="https://publications.waset.org/search?q=astrophysics." title=" astrophysics."> astrophysics.</a> </p> <a href="https://publications.waset.org/11056/an-efficient-computational-algorithm-for-solving-the-nonlinear-lane-emden-type-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/11056/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/11056/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/11056/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/11056/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/11056/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/11056/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/11056/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/11056/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/11056/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/11056/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/11056.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">3180</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">2631</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">2630</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> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2629</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">2628</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">2627</span> Power Series Solution to Sliding Velocity in Three-Dimensional Multibody Systems with Impact and Friction</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Hesham%20A.%20Elkaranshawy">Hesham A. Elkaranshawy</a>, <a href="https://publications.waset.org/search?q=Amr%20M.%20Abdelrazek"> Amr M. Abdelrazek</a>, <a href="https://publications.waset.org/search?q=Hosam%20M.%20Ezzat"> Hosam M. Ezzat</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The system of ordinary nonlinear differential equations describing sliding velocity during impact with friction for a three-dimensional rigid-multibody system is developed. No analytical solutions have been obtained before for this highly nonlinear system. Hence, a power series solution is proposed. Since the validity of this solution is limited to its convergence zone, a suitable time step is chosen and at the end of it a new series solution is constructed. For a case study, the trajectory of the sliding velocity using the proposed method is built using 6 time steps, which coincides with a Runge- Kutta solution using 38 time steps. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Impact%20with%20friction" title="Impact with friction">Impact with friction</a>, <a href="https://publications.waset.org/search?q=nonlinear%20ordinary%20differential%0D%0Aequations" title=" nonlinear ordinary differential equations"> nonlinear ordinary differential equations</a>, <a href="https://publications.waset.org/search?q=power%20series%20solutions" title=" power series solutions"> power series solutions</a>, <a href="https://publications.waset.org/search?q=rough%20collision." title=" rough collision."> rough collision.</a> </p> <a href="https://publications.waset.org/10002452/power-series-solution-to-sliding-velocity-in-three-dimensional-multibody-systems-with-impact-and-friction" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10002452/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10002452/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10002452/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10002452/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10002452/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10002452/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10002452/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10002452/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10002452/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10002452/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10002452.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">1916</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">2626</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">1363</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">2625</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">2624</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">2623</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">1480</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">2622</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">2621</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">2620</span> Exp-Function Method for Finding Some Exact Solutions of Rosenau Kawahara and Rosenau Korteweg-de Vries Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Ehsan%20Mahdavi">Ehsan Mahdavi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, we apply the Exp-function method to Rosenau-Kawahara and Rosenau-KdV equations. Rosenau-Kawahara equation is the combination of the Rosenau and standard Kawahara equations and Rosenau-KdV equation is the combination of the Rosenau and standard KdV equations. These equations are nonlinear partial differential equations (NPDE) which play an important role in mathematical physics. Exp-function method is easy, succinct and powerful to implement to nonlinear partial differential equations arising in mathematical physics. We mainly try to present an application of Exp-function method and offer solutions for common errors wich occur during some of the recent works.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Exp-function%20method" title="Exp-function method">Exp-function method</a>, <a href="https://publications.waset.org/search?q=Rosenau%20Kawahara%20equation" title=" Rosenau Kawahara equation"> Rosenau Kawahara equation</a>, <a href="https://publications.waset.org/search?q=Rosenau%20Korteweg-de%20Vries%20equation" title=" Rosenau Korteweg-de Vries equation"> Rosenau Korteweg-de Vries equation</a>, <a href="https://publications.waset.org/search?q=nonlinear%20partial%20differential%0D%0Aequation." title=" nonlinear partial differential equation."> nonlinear partial differential equation.</a> </p> <a href="https://publications.waset.org/9999253/exp-function-method-for-finding-some-exact-solutions-of-rosenau-kawahara-and-rosenau-korteweg-de-vries-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/9999253/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/9999253/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/9999253/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/9999253/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/9999253/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/9999253/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/9999253/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/9999253/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/9999253/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/9999253/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/9999253.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">2058</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">2619</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">2618</span> Solution of Nonlinear Second-Order Pantograph Equations via Differential Transformation Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Nemat%20Abazari">Nemat Abazari</a>, <a href="https://publications.waset.org/search?q=Reza%20Abazari"> Reza Abazari</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this work, we successfully extended one-dimensional differential transform method (DTM), by presenting and proving some theorems, to solving nonlinear high-order multi-pantograph equations. This technique provides a sequence of functions which converges to the exact solution of the problem. Some examples are given to demonstrate the validity and applicability of the present method and a comparison is made with existing results.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Nonlinear%20multi-pantograph%20equation" title="Nonlinear multi-pantograph equation">Nonlinear multi-pantograph equation</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=differential%20transformation%20method" title=" differential transformation method"> differential transformation method</a>, <a href="https://publications.waset.org/search?q=proportional%20delay%20conditions" title=" proportional delay conditions"> proportional delay conditions</a>, <a href="https://publications.waset.org/search?q=closed%20form%20solution." title=" closed form solution."> closed form solution.</a> </p> <a href="https://publications.waset.org/10520/solution-of-nonlinear-second-order-pantograph-equations-via-differential-transformation-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10520/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10520/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10520/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10520/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10520/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10520/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10520/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10520/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10520/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10520/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10520.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">2559</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">2617</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">1482</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">2616</span> Rational Chebyshev Tau Method for Solving Natural Convection of Darcian Fluid About a Vertical Full Cone Embedded in Porous Media Whit a Prescribed Wall Temperature</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Kourosh%20Parand">Kourosh Parand</a>, <a href="https://publications.waset.org/search?q=Zahra%20Delafkar"> Zahra Delafkar</a>, <a href="https://publications.waset.org/search?q=Fatemeh%20Baharifard"> Fatemeh Baharifard</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>The problem of natural convection about a cone embedded in a porous medium at local Rayleigh numbers based on the boundary layer approximation and the Darcy-s law have been studied before. Similarity solutions for a full cone with the prescribed wall temperature or surface heat flux boundary conditions which is the power function of distance from the vertex of the inverted cone give us a third-order nonlinear differential equation. In this paper, an approximate method for solving higher-order ordinary differential equations is proposed. The approach is based on a rational Chebyshev Tau (RCT) method. The operational matrices of the derivative and product of rational Chebyshev (RC) functions are presented. These matrices together with the Tau method are utilized to reduce the solution of the higher-order ordinary differential equations to the solution of a system of algebraic equations. We also present the comparison of this work with others and show that the present method is applicable.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Tau%20method" title="Tau method">Tau method</a>, <a href="https://publications.waset.org/search?q=semi-infinite" title=" semi-infinite"> semi-infinite</a>, <a href="https://publications.waset.org/search?q=nonlinear%20ODE" title=" nonlinear ODE"> nonlinear ODE</a>, <a href="https://publications.waset.org/search?q=rational%20Chebyshev" title=" rational Chebyshev"> rational Chebyshev</a>, <a href="https://publications.waset.org/search?q=porous%20media." title=" porous media."> porous media.</a> </p> <a href="https://publications.waset.org/2817/rational-chebyshev-tau-method-for-solving-natural-convection-of-darcian-fluid-about-a-vertical-full-cone-embedded-in-porous-media-whit-a-prescribed-wall-temperature" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/2817/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/2817/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/2817/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/2817/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/2817/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/2817/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/2817/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/2817/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/2817/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/2817/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/2817.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">1933</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">2615</span> Research of Amplitude-Frequency Characteristics of Nonlinear Oscillations of the Interface of Two-Layered Liquid</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Win%20Ko%20Ko">Win Ko Ko</a>, <a href="https://publications.waset.org/search?q=A.%20N.%20Temnov"> A. N. Temnov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>The problem of nonlinear oscillations of a two-layer liquid completely filling a limited volume is considered. Using two basic asymmetric harmonics excited in two mutually perpendicular planes, ordinary differential equations of nonlinear oscillations of the interface of a two-layer liquid are investigated. In this paper, hydrodynamic coefficients of linear and nonlinear problems in integral relations were determined. As a result, the instability regions of forced oscillations of a two-layered liquid in a cylindrical tank occurring in the plane of action of the disturbing force are constructed, as well as the dynamic instability regions of the parametric resonance for different ratios of densities of the upper and lower liquids depending on the amplitudes of liquids from the excitations frequencies. Steady-state regimes of fluid motion were found in the regions of dynamic instability of the initial oscillation form. The Bubnov-Galerkin method is used to construct instability regions for approximate solution of nonlinear differential equations.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Hydrodynamic%20coefficients" title="Hydrodynamic coefficients">Hydrodynamic coefficients</a>, <a href="https://publications.waset.org/search?q=instability%20region" title=" instability region"> instability region</a>, <a href="https://publications.waset.org/search?q=nonlinear%20oscillations" title=" nonlinear oscillations"> nonlinear oscillations</a>, <a href="https://publications.waset.org/search?q=resonance%20frequency" title=" resonance frequency"> resonance frequency</a>, <a href="https://publications.waset.org/search?q=two-layered%20liquid." title=" two-layered liquid. "> two-layered liquid. </a> </p> <a href="https://publications.waset.org/10011015/research-of-amplitude-frequency-characteristics-of-nonlinear-oscillations-of-the-interface-of-two-layered-liquid" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10011015/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10011015/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10011015/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10011015/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10011015/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10011015/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10011015/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10011015/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10011015/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10011015/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10011015.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">565</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">2614</span> Solution of Density Dependent Nonlinear Reaction-Diffusion Equation Using Differential Quadrature Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=G%C3%BClnihal%20Meral">Gülnihal Meral</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this study, the density dependent nonlinear reactiondiffusion equation, which arises in the insect dispersal models, is solved using the combined application of differential quadrature method(DQM) and implicit Euler method. The polynomial based DQM is used to discretize the spatial derivatives of the problem. The resulting time-dependent nonlinear system of ordinary differential equations(ODE-s) is solved by using implicit Euler method. The computations are carried out for a Cauchy problem defined by a onedimensional density dependent nonlinear reaction-diffusion equation which has an exact solution. The DQM solution is found to be in a very good agreement with the exact solution in terms of maximum absolute error. The DQM solution exhibits superior accuracy at large time levels tending to steady-state. Furthermore, using an implicit method in the solution procedure leads to stable solutions and larger time steps could be used. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Density%20Dependent%20Nonlinear%20Reaction-Diffusion%20Equation" title="Density Dependent Nonlinear Reaction-Diffusion Equation">Density Dependent Nonlinear Reaction-Diffusion Equation</a>, <a href="https://publications.waset.org/search?q=Differential%20Quadrature%20Method" title=" Differential Quadrature Method"> Differential Quadrature Method</a>, <a href="https://publications.waset.org/search?q=Implicit%20Euler%20Method." title=" Implicit Euler Method."> Implicit Euler Method.</a> </p> <a href="https://publications.waset.org/8909/solution-of-density-dependent-nonlinear-reaction-diffusion-equation-using-differential-quadrature-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/8909/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/8909/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/8909/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/8909/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/8909/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/8909/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/8909/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/8909/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/8909/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/8909/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/8909.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">2273</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">2613</span> Radiation Effect on MHD Casson Fluid Flow over a Power-Law Stretching Sheet with Chemical Reaction</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Motahar%20Reza">Motahar Reza</a>, <a href="https://publications.waset.org/search?q=Rajni%20Chahal"> Rajni Chahal</a>, <a href="https://publications.waset.org/search?q=Neha%20Sharma"> Neha Sharma</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>This article addresses the boundary layer flow and heat transfer of Casson fluid over a nonlinearly permeable stretching surface with chemical reaction in the presence of variable magnetic field. The effect of thermal radiation is considered to control the rate of heat transfer at the surface. Using similarity transformations, the governing partial differential equations of this problem are reduced into a set of non-linear ordinary differential equations which are solved by finite difference method. It is observed that the velocity at fixed point decreases with increasing the nonlinear stretching parameter but the temperature increases with nonlinear stretching parameter.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Boundary%20layer%20flow" title="Boundary layer flow">Boundary layer flow</a>, <a href="https://publications.waset.org/search?q=nonlinear%20stretching" title=" nonlinear stretching"> nonlinear stretching</a>, <a href="https://publications.waset.org/search?q=Casson%20fluid" title=" Casson fluid"> Casson fluid</a>, <a href="https://publications.waset.org/search?q=heat%20transfer" title=" heat transfer"> heat transfer</a>, <a href="https://publications.waset.org/search?q=radiation." title=" radiation."> radiation.</a> </p> <a href="https://publications.waset.org/10004434/radiation-effect-on-mhd-casson-fluid-flow-over-a-power-law-stretching-sheet-with-chemical-reaction" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10004434/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10004434/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10004434/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10004434/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10004434/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10004434/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10004434/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10004434/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10004434/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10004434/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10004434.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">1790</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">2612</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">2611</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">2610</span> Numerical Study of Some Coupled PDEs by using Differential Transformation Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Reza%20Abazari">Reza Abazari</a>, <a href="https://publications.waset.org/search?q=Rasool%20Abazari"> Rasool Abazari</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, the two-dimension differential transformation method (DTM) is employed to obtain the closed form solutions of the three famous coupled partial differential equation with physical interest namely, the coupled Korteweg-de Vries(KdV) equations, the coupled Burgers equations and coupled nonlinear Schrödinger equation. We begin by showing that how the differential transformation method applies to a linear and non-linear part of any PDEs and apply on these coupled PDEs to illustrate the sufficiency of the method for this kind of nonlinear differential equations. The results obtained are in good agreement with the exact solution. These results show that the technique introduced here is accurate and easy to apply.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Coupled%20Korteweg-de%20Vries%28KdV%29%20equation" title="Coupled Korteweg-de Vries(KdV) equation">Coupled Korteweg-de Vries(KdV) equation</a>, <a href="https://publications.waset.org/search?q=Coupled%20Burgers%20equation" title=" Coupled Burgers equation"> Coupled Burgers equation</a>, <a href="https://publications.waset.org/search?q=Coupled%20Schr%C3%B6dinger%20equation" title=" Coupled Schrödinger equation"> Coupled Schrödinger equation</a>, <a href="https://publications.waset.org/search?q=differential%20transformation%20method." title=" differential transformation method."> differential transformation method.</a> </p> <a href="https://publications.waset.org/9113/numerical-study-of-some-coupled-pdes-by-using-differential-transformation-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/9113/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/9113/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/9113/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/9113/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/9113/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/9113/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/9113/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/9113/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/9113/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/9113/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/9113.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">3001</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">2609</span> Numerical Algorithms for Solving a Type of Nonlinear Integro-Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Shishen%20Xie">Shishen Xie</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this article two algorithms, one based on variation iteration method and the other on Adomian's decomposition method, are developed to find the numerical solution of an initial value problem involving the non linear integro differantial equation where R is a nonlinear operator that contains partial derivatives with respect to x. Special cases of the integro-differential equation are solved using the algorithms. The numerical solutions are compared with analytical solutions. The results show that these two methods are efficient and accurate with only two or three iterations</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=variation%20iteration%20method" title="variation iteration method">variation iteration method</a>, <a href="https://publications.waset.org/search?q=decomposition%20method" title=" decomposition method"> decomposition method</a>, <a href="https://publications.waset.org/search?q=nonlinear%20integro-differential%20equations" title="nonlinear integro-differential equations">nonlinear integro-differential equations</a> </p> <a href="https://publications.waset.org/1281/numerical-algorithms-for-solving-a-type-of-nonlinear-integro-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/1281/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/1281/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/1281/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/1281/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/1281/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/1281/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/1281/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/1281/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/1281/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/1281/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/1281.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">2126</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">2608</span> ψ-exponential Stability for Non-linear Impulsive Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Bhanu%20Gupta">Bhanu Gupta</a>, <a href="https://publications.waset.org/search?q=Sanjay%20K.%20Srivastava"> Sanjay K. Srivastava</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we shall present sufficient conditions for the ψ-exponential stability of a class of nonlinear impulsive differential equations. We use the Lyapunov method with functions that are not necessarily differentiable. In the last section, we give some examples to support our theoretical results. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Exponential%20stability" title="Exponential stability">Exponential stability</a>, <a href="https://publications.waset.org/search?q=globally%20exponential%20stability" title=" globally exponential stability"> globally exponential stability</a>, <a href="https://publications.waset.org/search?q=impulsive%20differential%20equations" title="impulsive differential equations">impulsive differential equations</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=%CF%88-stability." title=" ψ-stability."> ψ-stability.</a> </p> <a href="https://publications.waset.org/5781/ps-exponential-stability-for-non-linear-impulsive-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/5781/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/5781/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/5781/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/5781/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/5781/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/5781/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/5781/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/5781/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/5781/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/5781/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/5781.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">3935</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">2607</span> Numerical Study of a Class of Nonlinear Partial Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Kholod%20M.%20Abu-Alnaja">Kholod M. Abu-Alnaja</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work, we derive two numerical schemes for solving a class of nonlinear partial differential equations. The first method is of second order accuracy in space and time directions, the scheme is unconditionally stable using Von Neumann stability analysis, the scheme produced a nonlinear block system where Newton-s method is used to solve it. The second method is of fourth order accuracy in space and second order in time. The method is unconditionally stable and Newton's method is used to solve the nonlinear block system obtained. The exact single soliton solution and the conserved quantities are used to assess the accuracy and to show the robustness of the schemes. The interaction of two solitary waves for different parameters are also discussed. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Crank-Nicolson%20Scheme" title="Crank-Nicolson Scheme">Crank-Nicolson Scheme</a>, <a href="https://publications.waset.org/search?q=Douglas%20Scheme" title=" Douglas Scheme"> Douglas Scheme</a>, <a href="https://publications.waset.org/search?q=Partial%0ADifferential%20Equations" title=" Partial Differential Equations"> Partial Differential Equations</a> </p> <a href="https://publications.waset.org/2774/numerical-study-of-a-class-of-nonlinear-partial-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/2774/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/2774/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/2774/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/2774/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/2774/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/2774/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/2774/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/2774/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/2774/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/2774/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/2774.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">1453</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">2606</span> Perturbation Based Modelling of Differential Amplifier Circuit</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Rahul%20Bansal">Rahul Bansal</a>, <a href="https://publications.waset.org/search?q=Sudipta%20Majumdar"> Sudipta Majumdar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents the closed form nonlinear expressions of bipolar junction transistor (BJT) differential amplifier (DA) using perturbation method. Circuit equations have been derived using Kirchhoff’s voltage law (KVL) and Kirchhoff’s current law (KCL). The perturbation method has been applied to state variables for obtaining the linear and nonlinear terms. The implementation of the proposed method is simple. The closed form nonlinear expressions provide better insights of physical systems. The derived equations can be used for signal processing applications. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Differential%20amplifier" title="Differential amplifier">Differential amplifier</a>, <a href="https://publications.waset.org/search?q=perturbation%20method" title=" perturbation method"> perturbation method</a>, <a href="https://publications.waset.org/search?q=Taylor%0D%0Aseries." title=" Taylor series."> Taylor series.</a> </p> <a href="https://publications.waset.org/10009006/perturbation-based-modelling-of-differential-amplifier-circuit" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10009006/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10009006/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10009006/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10009006/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10009006/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10009006/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10009006/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10009006/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10009006/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10009006/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10009006.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">1017</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">2605</span> Equations of Pulse Propagation in Three-Layer Structure of As2S3 Chalcogenide Plasmonic Nano-Waveguides</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Leila%20Motamed-Jahromi">Leila Motamed-Jahromi</a>, <a href="https://publications.waset.org/search?q=Mohsen%20Hatami"> Mohsen Hatami</a>, <a href="https://publications.waset.org/search?q=Alireza%20Keshavarz"> Alireza Keshavarz </a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>This research aims at obtaining the equations of pulse propagation in nonlinear plasmonic waveguides created with As<sub>2</sub>S<sub>3</sub> chalcogenide materials. Via utilizing Helmholtz equation and first-order perturbation theory, two components of electric field are determined within frequency domain. Afterwards, the equations are formulated in time domain. The obtained equations include two coupled differential equations that considers nonlinear dispersion<span dir="RTL">.</span></p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Nonlinear%20optics" title="Nonlinear optics">Nonlinear optics</a>, <a href="https://publications.waset.org/search?q=propagation%20equation" title=" propagation equation"> propagation equation</a>, <a href="https://publications.waset.org/search?q=plasmonic%20waveguide." title=" plasmonic waveguide."> plasmonic waveguide.</a> </p> <a href="https://publications.waset.org/10005672/equations-of-pulse-propagation-in-three-layer-structure-of-as2s3-chalcogenide-plasmonic-nano-waveguides" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10005672/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10005672/bibtex" target="_blank" rel="nofollow" class="btn btn-primary 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