Document Zbl 1217.65155

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H.</a>; <a href="/authors/abd-elhameed.waleed-m" title="Author Profile">Abd-Elhameed, W. M.</a></div> <h2 class="title"> <strong>New algorithm for the numerical solutions of nonlinear third-order differential equations using Jacobi-Gauss collocation method.</strong> <i>(English)</i> <a class="label nowrap" href="/1217.65155">Zbl 1217.65155</a> </h2> <div class="source"> <a href="/serials/2235" title="Journal Profile">Math. Probl. Eng.</a> <a href="/?q=in%3A271595" title="Articles in this Issue">2011, Article ID 837218, 14 p. (2011)</a>. </div> <div class="abstract">Summary: A new algorithm for solving the general nonlinear third-order differential equation is developed by means of a shifted Jacobi-Gauss collocation spectral method. The shifted Jacobi-Gauss points are used as collocation nodes. Numerical examples are included to demonstrate the validity and applicability of the proposed algorithm, and some comparisons are made with the existing results. The method is easy to implement and yields very accurate results.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A5904922">Cited in <strong>25</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A65L60" title="MSC2020">65L60</a> </td> <td class="space"> Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65L10" title="MSC2020">65L10</a> </td> <td class="space"> Numerical solution of boundary value problems involving ordinary differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A34B15" title="MSC2020">34B15</a> </td> <td class="space"> Nonlinear boundary value problems for ordinary differential equations </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aalgorithm">algorithm</a>; <a href="/?q=ut%3Anonlinear+third-order+differential+equation">nonlinear third-order differential equation</a>; <a href="/?q=ut%3AJacobi-Gauss+collocation+spectral+method">Jacobi-Gauss collocation spectral method</a>; <a href="/?q=ut%3Anumerical+examples">numerical examples</a></div> <div class="software"> <h3>Software:</h3><a href="/software/558">Matlab</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1217.65155" data-ciurl="/ci/05904922" data-biburl="/bibtex/05904922.bib" data-amsurl="/amsrefs/05904922.bib" data-xmlurl="/xml/05904922.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/05904922.pdf" title="Zbl 1217.65155 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1155/2011/837218" aria-label="DOI for “New algorithm for the numerical solutions of nonlinear third-order differential equations using Jacobi-Gauss collocation method”" title="10.1155/2011/837218">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://eudml.org/doc/229863" title="Open Access at EuDML">EuDML</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">C. 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