Document Zbl 1540.65391

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Comput. Simul.</a> <a href="/?q=in%3A472373" title="Articles in this Issue">188, 60-76 (2021)</a>. </div> <div class="abstract">Summary: In this article, a mixed element algorithm is presented to look for the numerical solution for a class of nonlinear wave model with the Caputo fractional derivative. By introducing two auxiliary functions and reducing order technique of fractional derivative, the studied model with high-order derivative in time is transformed into a coupled system including three lower order equations. Next, a fully discrete mixed element algorithm is formulated, where the temporal direction is approximated by a second-order scheme. The stability analysis of the proposed mixed scheme is done and optimal error estimates for three functions are derived. Finally, the numerical tests are carried out to verify the theory results.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7428988">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%3A65M60" title="MSC2020">65M60</a> </td> <td class="space"> Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35R11" title="MSC2020">35R11</a> </td> <td class="space"> Fractional partial differential 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><tr> <td> <a class="mono" href="/classification/?q=cc%3A65M15" title="MSC2020">65M15</a> </td> <td class="space"> Error bounds for initial value and initial-boundary value problems involving PDEs </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Atime+fractional+wave+model">time fractional wave model</a>; <a href="/?q=ut%3Amixed+element+algorithm">mixed element algorithm</a>; <a href="/?q=ut%3Astability">stability</a>; <a href="/?q=ut%3Aoptimal+error+estimates">optimal error estimates</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 1540.65391" data-ciurl="/ci/07428988" data-biburl="/bibtex/07428988.bib" data-amsurl="/amsrefs/07428988.bib" data-xmlurl="/xml/07428988.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07428988.pdf" title="Zbl 1540.65391 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.matcom.2021.03.038" aria-label="DOI for “Mixed finite element algorithm for a nonlinear time fractional wave model”" title="10.1016/j.matcom.2021.03.038">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">Alikhanov, A. 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