Document Zbl 1513.65284

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M.</a></div> <h2 class="title"> <strong>Convergence and numerical solution of nonlinear generalized Benjamin-Bona-Mahony-Burgers equation in 2D and 3D via generalized finite difference method.</strong> <i>(English)</i> <a class="label nowrap" href="/1513.65284">Zbl 1513.65284</a> </h2> <div class="source"> <a href="/serials/1585" title="Journal Profile">Int. J. Comput. Math.</a> <a href="/?q=in%3A484742" title="Articles in this Issue">99, No. 8, 1517-1537 (2022)</a>. </div> <div class="abstract">Summary: In this paper we present an application of the Generalized Finite Difference Method to solve the generalized nonlinear Benjamin-Bona-Mahony-Burgers equation in 2D and 3D. We provide two approaches to solving the BBMB equation. First, we directly use the explicit GFD scheme, and second, we transform the equation into a PDE system. In a further attempt we find criteria for the convergence of the fully explicit method using GFDM for the Benjamin-Bona-Mahony-Bourgers equation in 2D and 3D.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7563030">Cited in <strong>4</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%3A65N06" title="MSC2020">65N06</a> </td> <td class="space"> Finite difference methods for boundary value problems involving PDEs </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><tr> <td> <a class="mono" href="/classification/?q=cc%3A41A58" title="MSC2020">41A58</a> </td> <td class="space"> Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A92C17" title="MSC2020">92C17</a> </td> <td class="space"> Cell movement (chemotaxis, etc.) </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Ageneralized+finite+difference+method">generalized finite difference method</a>; <a href="/?q=ut%3Anonlinear+generalized+Benjamin-Bona-Mahony-Burgers+equation">nonlinear generalized Benjamin-Bona-Mahony-Burgers equation</a>; <a href="/?q=ut%3Aconvergence+analysis">convergence analysis</a>; <a href="/?q=ut%3Ameshless+methods">meshless methods</a>; <a href="/?q=ut%3APDE+system">PDE system</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 1513.65284" data-ciurl="/ci/07563030" data-biburl="/bibtex/07563030.bib" data-amsurl="/amsrefs/07563030.bib" data-xmlurl="/xml/07563030.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07563030.pdf" title="Zbl 1513.65284 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/10.1080/00207160.2021.1989423" aria-label="DOI for “Convergence and numerical solution of nonlinear generalized Benjamin-Bona-Mahony-Burgers equation in 2D and 3D via generalized finite difference method”" title="10.1080/00207160.2021.1989423">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">Arora, S.; Jain, R.; Kukreja, V. K., Solution of Benjamin-Bona-Mahony-Burgers equation using collocation method with quintic Hermite splines, Appl. Numer. Math., 154, 1-16 (2020) · <a href="/1437.65164" class="nowrap">Zbl 1437.65164</a></td> </tr><tr> <td>[2]</td> <td class="space">Benito, J. J.; García, A.; Gavete, L.; Negreanu, M.; Ureña, F.; Vargas, A. M., On the numerical solution to a parabolic-elliptic system with chemotactic and periodic terms using generalized finite differences, Eng. Anal. Bound. Elem., 113, 181-190 (2020) · <a href="/1464.92004" class="nowrap">Zbl 1464.92004</a></td> </tr><tr> <td>[3]</td> <td class="space">Benito, J. J.; García, A.; Gavete, L.; Negreanu, M.; Ureña, F.; Vargas, A. M., Solving a chemotaxis-haptotaxis system in 2D using generalized finite difference method, Comput. Math. Appl., 80, 762-777 (2020) · <a href="/1447.65069" class="nowrap">Zbl 1447.65069</a></td> </tr><tr> <td>[4]</td> <td class="space">Benito, J. 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Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none"> <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>

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