Document Zbl 1312.65138

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Calc. Appl. Anal.</a> <a href="/?q=in%3A313625" title="Articles in this Issue">16, No. 1, 9-25 (2013)</a>. </div> <div class="abstract">Summary: In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals $[0,1]$, $[1,2)$, $[0,2)$, $[0,3)$, $[2,3)$ and $[2,4)$, respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6440314">Cited in <strong>234</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%3A35R11" title="MSC2020">35R11</a> </td> <td class="space"> Fractional partial differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65M22" title="MSC2020">65M22</a> </td> <td class="space"> Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35L05" title="MSC2020">35L05</a> </td> <td class="space"> Wave equation </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Amulti-term+time+fractional+wave-diffusion+equations">multi-term time fractional wave-diffusion equations</a>; <a href="/?q=ut%3ACaputo+derivative">Caputo derivative</a>; <a href="/?q=ut%3Aa+power+law+wave+equation">a power law wave equation</a>; <a href="/?q=ut%3Afinite+difference+method">finite difference method</a>; <a href="/?q=ut%3Afractional+predictor-corrector+method">fractional predictor-corrector method</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 1312.65138" data-ciurl="/ci/06440314" data-biburl="/bibtex/06440314.bib" data-amsurl="/amsrefs/06440314.bib" data-xmlurl="/xml/06440314.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06440314.pdf" title="Zbl 1312.65138 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/10.2478/s13540-013-0002-2" aria-label="DOI for “Numerical methods for solving the multi-term time-fractional wave-diffusion equation”" title="10.2478/s13540-013-0002-2">DOI</a> <a class="btn btn-default btn-xs" type="button" href="http://europepmc.org/articles/pmc3679177" title="Full Text Link">Link</a> </div> <div class="sfx" style="float: right;"> <a href="https://creativecommons.org/licenses/by-nc-nd/3.0/" target="_blank" title="Open Access License" class="cc-license-link no-new-tab-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/cc.svg" alt="Creative Commons CC license icon" class="cc-license-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/by.svg" alt="Creative Commons BY license icon" class="cc-license-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/nc.svg" alt="Creative Commons NC license icon" class="cc-license-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/nd.svg" alt="Creative Commons ND license icon" class="cc-license-icon"> </a> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">B. 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