Document Zbl 1429.65182

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Math. Comput.</a> <a href="/?q=in%3A442730" title="Articles in this Issue">346, 385-394 (2019)</a>. </div> <div class="abstract">Summary: In this article, we propose a parameter-uniformly convergent numerical method for viscous Burgers’ equation. In order to find a numerical approximation to Burgers’ equation, we linearize the equation to obtain sequence of linear PDEs. The linear PDEs are solved by a finite difference scheme, which comprises of the backward-difference scheme for the time derivative and upwind finite difference scheme for the spatial derivatives. Layer-adapted nonuniform meshes are invoked at each time level to exhibit layer nature of the solution. The nonuniform meshes are obtained by equidistribution of a positive integrable monitor function, which involves the derivative of the solution. It is shown that the methods converges uniformly with respect to the perturbation parameter. Numerical experiments are carried out to validate the $\varepsilon $-uniform error estimate of $O(N^{-1} + \Delta t)$.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7136469">Cited in <strong>13</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A65M06" title="MSC2020">65M06</a> </td> <td class="space"> Finite difference methods for initial value and initial-boundary value problems involving PDEs </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35B25" title="MSC2020">35B25</a> </td> <td class="space"> Singular perturbations in context of PDEs </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35Q53" title="MSC2020">35Q53</a> </td> <td class="space"> KdV equations (Korteweg-de Vries equations) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65M12" title="MSC2020">65M12</a> </td> <td class="space"> Stability and convergence of numerical 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%3Asingularly+perturbed+parabolic+problem">singularly perturbed parabolic problem</a>; <a href="/?q=ut%3ABurgers%27+equation">Burgers’ equation</a>; <a href="/?q=ut%3Aboundary+layers">boundary layers</a>; <a href="/?q=ut%3Aequidistribution+grid">equidistribution grid</a>; <a href="/?q=ut%3Afinite+difference+scheme">finite difference scheme</a>; <a href="/?q=ut%3Auniform+convergence">uniform convergence</a></div> <div class="software"> <h3>Software:</h3><a href="/software/7938">MOVCOL</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 1429.65182" data-ciurl="/ci/07136469" data-biburl="/bibtex/07136469.bib" data-amsurl="/amsrefs/07136469.bib" data-xmlurl="/xml/07136469.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07136469.pdf" title="Zbl 1429.65182 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.amc.2018.10.049" aria-label="DOI for “An efficient robust numerical method for singularly perturbed Burgers' equation”" title="10.1016/j.amc.2018.10.049">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">Abazari, R.; Borhanifar, A., Numerical study of the solution of the burgers and coupled burgers equations by a differential transformation method, Comput. 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