Document Zbl 1144.65057

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Math. Comput.</a> <a href="/?q=in%3A218290" title="Articles in this Issue">198, No. 2, 754-769 (2008)</a>. </div> <div class="abstract">This paper deals with a fractional reaction-subdiffusion equation (FR-subDE) in a bounded domain in which both the motion and the reaction terms are affected by the subdiffusive character of the process. An implicit finite difference method (IFDM) and an explicit finite difference method (EFDM) for the FR-subDE are proposed. The stability and the convergence of the IFDM and EFDM are discussed using a Fourier analysis and the solvability of the IFDM is proved. A comparison between the exact solution and the two numerical solutions shows the agreement of the theoretical analysis with the numerical results.<div class="reviewer"> Reviewer: <a href="/authors/?q=rv%3A6273">Ruxandra Stavre (Bucureşti)</a></div> <div class="clearfix"></div></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A5268336">Cited in <strong>102</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%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%3A35K57" title="MSC2020">35K57</a> </td> <td class="space"> Reaction-diffusion equations </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aspace-time+fractional+derivatives">space-time fractional derivatives</a>; <a href="/?q=ut%3Astability">stability</a>; <a href="/?q=ut%3Aconvergence">convergence</a>; <a href="/?q=ut%3Afractional+reaction-subdiffusion+equation">fractional reaction-subdiffusion equation</a>; <a href="/?q=ut%3Aexplicit+finite+difference+method">explicit finite difference method</a>; <a href="/?q=ut%3Aimplicit+finite+difference+method">implicit finite difference method</a>; <a href="/?q=ut%3Anumerical+results">numerical results</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 1144.65057" data-ciurl="/ci/05268336" data-biburl="/bibtex/05268336.bib" data-amsurl="/amsrefs/05268336.bib" data-xmlurl="/xml/05268336.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/05268336.pdf" title="Zbl 1144.65057 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.amc.2007.09.020" aria-label="DOI for “Finite difference methods and a Fourier analysis for the fractional reaction-subdiffusion equation”" title="10.1016/j.amc.2007.09.020">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://eprints.qut.edu.au/224083/1/14755a.pdf" title="Full Text Link">Link</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Gorenflo, R.; Mainardi, F., Random walk models for space-fractional diffusion processes, Fract. 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