A Family of Zero Stable Block Integrator for the Solutions of Ordinary Differential Equations

<!DOCTYPE html> <html lang="en" dir="ltr"> <head>  <script async src="https://www.googletagmanager.com/gtag/js?id=G-P63WKM1TM1"></script> <script> window.dataLayer = window.dataLayer || []; function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-P63WKM1TM1'); </script>  <script type="text/javascript" > (function(m,e,t,r,i,k,a){m[i]=m[i]||function(){(m[i].a=m[i].a||[]).push(arguments)}; m[i].l=1*new Date(); for (var j = 0; j < document.scripts.length; j++) {if (document.scripts[j].src === r) { return; }} k=e.createElement(t),a=e.getElementsByTagName(t)[0],k.async=1,k.src=r,a.parentNode.insertBefore(k,a)}) (window, document, "script", "https://mc.yandex.ru/metrika/tag.js", "ym"); ym(55165297, "init", { clickmap:false, trackLinks:true, accurateTrackBounce:true, webvisor:false }); </script> <noscript><div><img src="https://mc.yandex.ru/watch/55165297" style="position:absolute; left:-9999px;" alt="" /></div></noscript>    <title>A Family of Zero Stable Block Integrator for the Solutions of Ordinary Differential Equations</title> <meta name="description" content="A Family of Zero Stable Block Integrator for the Solutions of Ordinary Differential Equations"> <meta name="keywords" content="Block Method, Hybrid, Linear Multistep Method, Self – starting, Special Second Order."> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <meta name="citation_title" content="A Family of Zero Stable Block Integrator for the Solutions of Ordinary Differential Equations"> <meta name="citation_author" content="A. M. Sagir"> <meta name="citation_publication_date" content="2013/06/27"> <meta name="citation_journal_title" content="International Journal of Mathematical and Computational Sciences"> <meta name="citation_volume" content="7"> <meta name="citation_issue" content="6"> <meta name="citation_firstpage" content="1020"> <meta name="citation_lastpage" content="1025"> <meta name="citation_pdf_url" content="https://publications.waset.org/10892/pdf"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> <button class="d-block d-lg-none navbar-toggler ml-auto" type="button" data-toggle="collapse" data-target="#navbarMenu" aria-controls="navbarMenu" aria-expanded="false" aria-label="Toggle navigation"> <span class="navbar-toggler-icon"></span> </button> <div class="w-100"> <div class="d-none d-lg-flex flex-row-reverse"> <form method="get" action="https://waset.org/search" class="form-inline my-2 my-lg-0"> <input class="form-control mr-sm-2" type="search" placeholder="Search Conferences" value="" name="q" aria-label="Search"> <button class="btn btn-light my-2 my-sm-0" type="submit"><i class="fas fa-search"></i></button> </form> </div> <div class="collapse navbar-collapse mt-1" id="navbarMenu"> <ul class="navbar-nav ml-auto align-items-center" id="mainNavMenu"> <li class="nav-item"> <a class="nav-link" href="https://waset.org/conferences" title="Conferences in 2024/2025/2026">Conferences</a> </li> <li class="nav-item"> <a class="nav-link" href="https://waset.org/disciplines" title="Disciplines">Disciplines</a> </li> <li class="nav-item"> <a class="nav-link" href="https://waset.org/committees" rel="nofollow">Committees</a> </li> <li class="nav-item dropdown"> <a class="nav-link dropdown-toggle" href="#" id="navbarDropdownPublications" role="button" data-toggle="dropdown" aria-haspopup="true" aria-expanded="false"> Publications </a> <div class="dropdown-menu" aria-labelledby="navbarDropdownPublications"> <a class="dropdown-item" href="https://publications.waset.org/abstracts">Abstracts</a> <a class="dropdown-item" href="https://publications.waset.org">Periodicals</a> <a class="dropdown-item" href="https://publications.waset.org/archive">Archive</a> </div> </li> <li class="nav-item"> <a class="nav-link" href="https://waset.org/page/support" title="Support">Support</a> </li> </ul> </div> </div> </nav> </div> </header> <main> <div class="container mt-4"> <div class="row"> <div class="col-md-9 mx-auto"> <form method="get" action="https://publications.waset.org/search"> <div id="custom-search-input"> <div class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value=""> <input type="submit" class="btn_search" value="Search"> </div> </div> </form> </div> </div> <div class="row mt-3"> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Commenced</strong> in January 2007</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Frequency:</strong> Monthly</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Edition:</strong> International</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Paper Count:</strong> 33093</div> </div> </div> </div> <div class="card publication-listing mt-3 mb-3"> <h5 class="card-header" style="font-size:.9rem">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. <iframe src="https://publications.waset.org/10892.pdf" style="width:100%; height:400px;" frameborder="0"></iframe> <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> <p class="card-text"><strong>Digital Object Identifier (DOI):</strong> <a href="https://doi.org/10.5281/zenodo.1076126" target="_blank">doi.org/10.5281/zenodo.1076126</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> <p class="card-text"><strong>References:</strong></p> <br>[1] S.O. Fatunla, Block Method for Second Order Initial Value Problem. International Journal of Computer Mathematics, England. Vol. 4, 1991, pp 55 - 63. <br>[2] S.O. Fatunla, Higher Order parallel Methods for Second Order ODEs. Proceedings of the fifth international conference on scientific computing, 1994, pp 61 -67. <br>[3] J. D. Lambert, Computational Methods in Ordinary Differential Equations (John Willey and Sons, New York, USA, 1973). <br>[4] P. Onumanyi, D.O. Awoyemi, S.N. Jator and U.W. Sirisena, New linear Multistep with Continuous Coefficient for first order initial value problems. Journal of Mathematical Society, 13, 1994, pp 37 - 51. <br>[5] D.O. Awoyemi, A class of Continuous Stormer - Cowell Type Methods for Special Second Order Ordinary Differential Equations. Journal of Nigerian Mathematical Society Vol. 5, Nos. 1 & 2, 1998, pp100 - 108. <br>[6] I. Fudziah L. K. Yap. and O. Mohammad, Explicit and Implicit 3 - point Block Methods for Solving Special Second Order Ordinary Differential Equations Directly. International Journal of math. Analysis, Vol. 3, 2009, pp 239 - 254. <br>[7] K.R. Adeboye , A superconvergent H2 - Galerkin method for the solution of Boundary Value Problems. Proceedings National Mathematical Centre, Abuja, Nigeria. Vol. 1 no.1, 2000, pp 118 - 124, ISBN 978 - 35488 - 0 - 2 . <br>[8] P. Henrici, Discrete Variable Methods for ODEs. 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A Family of Zero Stable Block Integrator for the Solutions of Ordinary Differential Equations