Document Zbl 1550.49031

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J. Nonlinear Sci. Numer. Simul.</a> <a href="/?q=in%3A482481" title="Articles in this Issue">23, No. 2, 273-281 (2022)</a>. </div> <div class="abstract">Summary: In this paper we present callocation method for solving the problems in the calculus of variation (CV) using multiquadratic radial basis functions (MQRBFs). In this method we use the Gauss quadrature rule for approximating the integral in CV problems. The effects of the shape parameter of MQRBFs on the convergence of the method have been discussed. Illustrative examples are included to evaluate the capability of the proposed method.</div> <div class="clear"></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A49M27" title="MSC2020">49M27</a> </td> <td class="space"> Decomposition methods </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A49J05" title="MSC2020">49J05</a> </td> <td class="space"> Existence theories for free problems in one independent variable </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A49M37" title="MSC2020">49M37</a> </td> <td class="space"> Numerical methods based on nonlinear programming </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65D12" title="MSC2020">65D12</a> </td> <td class="space"> Numerical radial basis function approximation </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Abrachistochrone+problem">brachistochrone problem</a>; <a href="/?q=ut%3Acalculus+of+variation">calculus of variation</a>; <a href="/?q=ut%3Aerror+analysis">error analysis</a>; <a href="/?q=ut%3Amultiquadric+radial+basis+function">multiquadric radial basis function</a>; <a href="/?q=ut%3Anumerical+results">numerical results</a>; <a href="/?q=ut%3ARBF">RBF</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 1550.49031" data-ciurl="/ci/07533169" data-biburl="/bibtex/07533169.bib" data-amsurl="/amsrefs/07533169.bib" data-xmlurl="/xml/07533169.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07533169.pdf" title="Zbl 1550.49031 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/10.1515/ijnsns-2018-0220" aria-label="DOI for “Solving calculus of variation problems via multiquadric radial basis function method with optimal shape parameter”" title="10.1515/ijnsns-2018-0220">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">D. 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