Document Zbl 1404.65085

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Numer. Math.</a> <a href="/?q=in%3A418802" title="Articles in this Issue">135, 30-46 (2019)</a>. </div> <div class="abstract">Summary: In this paper, we focus our attention on the development of the high-order numerical algorithm for the time-space tempered fractional diffusion-wave equation in two spatial dimensions. Based on the fourth-order fractional-compact difference operator, a new difference scheme with convergence order $\mathcal{O}(\tau^2 + h_1^4 + h_2^4)$ is derived, where $\tau$ is the temporal stepsize, $h_1$ and $h_2$ are the spatial stepsizes, respectively. The stability and convergence of the algorithm are investigated by the energy method and numerical experiment is carried out to verify the feasibility of the numerical algorithm.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6969461">Cited in <strong>18</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%3A26A33" title="MSC2020">26A33</a> </td> <td class="space"> Fractional derivatives and integrals </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%3Atime-space+tempered+fractional+diffusion-wave+equation">time-space tempered fractional diffusion-wave equation</a>; <a href="/?q=ut%3ARiesz+derivative">Riesz derivative</a>; <a href="/?q=ut%3Afractional-compact+difference+operator">fractional-compact difference operator</a>; <a href="/?q=ut%3Atempered+fractional+integral">tempered fractional integral</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 1404.65085" data-ciurl="/ci/06969461" data-biburl="/bibtex/06969461.bib" data-amsurl="/amsrefs/06969461.bib" data-xmlurl="/xml/06969461.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06969461.pdf" title="Zbl 1404.65085 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.apnum.2018.08.005" aria-label="DOI for “A high-order numerical algorithm for two-dimensional time-space tempered fractional diffusion-wave equation”" title="10.1016/j.apnum.2018.08.005">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">Bai, J.; Feng, X., Fractional-order anisotropic diffusion for image denoising, IEEE Trans. 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