Document Zbl 1447.65026

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Numer. Anal.</a> <a href="/?q=in%3A379987" title="Articles in this Issue">56, No. 2, 1112-1133 (2018)</a>. </div> <div class="abstract">The authors are concerned with stability and convergence of the $L1$ formula on nonuniform time grids for solving linear reaction-subdiffusion equations featuring the Caputo derivative. First, a discrete fractional Grönwall inequality is developed for the nonuniform $L1$ formula by introducing a discrete convolution kernel of Riemann-Liouville fractional integral. This discrete fractional inequality allows the authors to obtain a sharp error estimate reflecting the regularity of solution for a simple $L1$ scheme. Numerical experiments also presented to illustrate the theoretical findings.<div class="reviewer"> Reviewer: <a href="/authors/?q=rv%3A11577">Marius Ghergu (Dublin)</a></div> <div class="clearfix"></div></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=ci%3A6869999">Cited in <strong>1</strong> Review</a></div><div class="clear"><a href="/?q=rf%3A6869999">Cited in <strong>301</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%3A65M15" title="MSC2020">65M15</a> </td> <td class="space"> Error bounds for initial value and initial-boundary value problems involving PDEs </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35B65" title="MSC2020">35B65</a> </td> <td class="space"> Smoothness and regularity of solutions to 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></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Afractional+subdiffusion+equations">fractional subdiffusion equations</a>; <a href="/?q=ut%3Anonuniform+%5C%28L1%5C%29+formula">nonuniform $L1$ formula</a>; <a href="/?q=ut%3Adiscrete+fractional+Gr%C3%B6nwall+inequality">discrete fractional Grönwall inequality</a>; <a href="/?q=ut%3Aglobal+consistency+analysis">global consistency analysis</a>; <a href="/?q=ut%3Asharp+error+estimate">sharp error estimate</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 1447.65026" data-ciurl="/ci/06869999" data-biburl="/bibtex/06869999.bib" data-amsurl="/amsrefs/06869999.bib" data-xmlurl="/xml/06869999.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06869999.pdf" title="Zbl 1447.65026 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/10.1137/17M1131829" aria-label="DOI for “Sharp error estimate of the nonuniform L1 formula for linear reaction-subdiffusion equations”" title="10.1137/17M1131829">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">A.A. 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