Document Zbl 1155.65381

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H.</a>; <a href="/authors/temsah.r-s" title="Author Profile">Temsah, R. S.</a></div> <h2 class="title"> <strong>Numerical solutions of the generalized Kuramoto-Sivashinsky equation by Chebyshev spectral collocation methods.</strong> <i>(English)</i> <a class="label nowrap" href="/1155.65381">Zbl 1155.65381</a> </h2> <div class="source"> <a href="/serials/62" title="Journal Profile">Comput. Math. Appl.</a> <a href="/?q=in%3A227610" title="Articles in this Issue">56, No. 6, 1465-1472 (2008)</a>. </div> <div class="abstract">Summary: Chebyshev spectral collocation methods (known as El-Gendi method [<span class="zbmathjax-textit">S. E. El-Gendi</span>, Comput. J. 12, 282–287 (1969; <a href="/0198.50201">Zbl 0198.50201</a>)] and <span class="zbmathjax-textit">B. Mihaila</span> and <span class="zbmathjax-textit">I. Mihaila</span> [J. Phys. A, Math. Gen. 35, No. 3, 731–746 (2002; <a href="/1045.65070">Zbl 1045.65070</a>)]) are extended to deal with the generalized Kuramoto-Sivashinsky equation. The problem is reduced to a system of ordinary differential equations that are solved by combinations of backward differential formula and appropriate explicit schemes (implicit-explicit BDF methods [<span class="zbmathjax-textit">G. Akrivis</span> and <span class="zbmathjax-textit">Y.-S. Smyrlis</span>, Appl. Numer. Math. 51, No. 2–3, 151–169 (2004; <a href="/1057.65069">Zbl 1057.65069</a>)]. Good numerical results have been obtained and compared with the exact solutions.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A5528642">Cited in <strong>45</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A65M70" title="MSC2020">65M70</a> </td> <td class="space"> Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3AKuramoto-Sivashinsky+equation">Kuramoto-Sivashinsky equation</a>; <a href="/?q=ut%3Anumerical+solution">numerical solution</a>; <a href="/?q=ut%3AChebyshev+spectral+collocation+method">Chebyshev spectral collocation method</a></div><div class="keywords"> <h3>Citations:</h3><a href="/0198.50201">Zbl 0198.50201</a>; <a href="/1045.65070">Zbl 1045.65070</a>; <a href="/1057.65069">Zbl 1057.65069</a></div> <div class="software"> <h3>Software:</h3><a href="/software/12342">PDESpecialSolutions</a>; <a href="/software/42146">ATFM</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 1155.65381" data-ciurl="/ci/05528642" data-biburl="/bibtex/05528642.bib" data-amsurl="/amsrefs/05528642.bib" data-xmlurl="/xml/05528642.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/05528642.pdf" title="Zbl 1155.65381 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/10.1016/j.camwa.2008.03.013" aria-label="DOI for “Numerical solutions of the generalized Kuramoto-Sivashinsky equation by Chebyshev spectral collocation methods”" title="10.1016/j.camwa.2008.03.013">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">El-Gendi, S. 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