Document Zbl 1500.65034

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Comput.</a> <a href="/?q=in%3A486504" title="Articles in this Issue">91, No. 338, 2681-2714 (2022)</a>. </div> <div class="abstract">Summary: Stabilized Runge-Kutta methods are especially efficient for the numerical solution of large systems of stiff nonlinear differential equations because they are fully explicit. For semi-discrete parabolic problems, for instance, stabilized Runge-Kutta methods overcome the stringent stability condition of standard methods without sacrificing explicitness. However, when stiffness is only induced by a few components, as in the presence of spatially local mesh refinement, their efficiency deteriorates. To remove the crippling effect of a few severely stiff components on the entire system of differential equations, we derive a modified equation, whose stiffness solely depends on the remaining mildly stiff components. By applying stabilized Runge-Kutta methods to this modified equation, we then devise an explicit multirate Runge-Kutta-Chebyshev (mRKC) method whose stability conditions are independent of a few severely stiff components. Stability of the mRKC method is proved for a model problem, whereas its efficiency and usefulness are demonstrated through a series of numerical experiments.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7582811">Cited in <strong>6</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A65L04" title="MSC2020">65L04</a> </td> <td class="space"> Numerical methods for stiff equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65L06" title="MSC2020">65L06</a> </td> <td class="space"> Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65L20" title="MSC2020">65L20</a> </td> <td class="space"> Stability and convergence of numerical methods for ordinary differential equations </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Astabilized+Runge-Kutta+methods">stabilized Runge-Kutta methods</a>; <a href="/?q=ut%3Aexplicit+time+integrators">explicit time integrators</a>; <a href="/?q=ut%3Astiff+equations">stiff equations</a>; <a href="/?q=ut%3Amultirate+methods">multirate methods</a>; <a href="/?q=ut%3Alocal+time-stepping">local time-stepping</a>; <a href="/?q=ut%3Aparabolic+problems">parabolic problems</a>; <a href="/?q=ut%3AChebyshev+methods">Chebyshev methods</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 1500.65034" data-ciurl="/ci/07582811" data-biburl="/bibtex/07582811.bib" data-amsurl="/amsrefs/07582811.bib" data-xmlurl="/xml/07582811.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07582811.pdf" title="Zbl 1500.65034 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/10.1090/mcom/3753" aria-label="DOI for “Explicit stabilized multirate method for stiff differential equations”" title="10.1090/mcom/3753">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/2006.00744"title="Note: arXiv document may differ from published version">arXiv</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Abdulle, Assyr, Fourth order Chebyshev methods with recurrence relation, SIAM J. 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