Document Zbl 1295.65128

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R. Navid</a>; <a href="/authors/tohidi.emran" title="Author Profile">Tohidi, Emran</a></div> <h2 class="title"> <strong>The spectral method for solving systems of Volterra integral equations.</strong> <i>(English)</i> <a class="label nowrap" href="/1295.65128">Zbl 1295.65128</a> </h2> <div class="source"> <a href="/serials/2985" title="Journal Profile">J. Appl. Math. Comput.</a> <a href="/?q=in%3A334347" title="Articles in this Issue">40, No. 1-2, 477-497 (2012)</a>. </div> <div class="abstract"><div class="pre">Summary: This paper presents a high accurate and stable Legendre-collocation method for solving systems of Volterra integral equations (SVIEs) of the second kind. The method transforms the linear SVIEs into the associated matrix equation. In the nonlinear case, after applying our method we solve a system of nonlinear algebraic equations. Also, sufficient conditions for the existence and uniqueness of the linear SVIEs, in which the coefficient of the main term is a singular (or nonsingular) matrix, have been formulated. Several examples are included to illustrate the efficiency and accuracy of the proposed technique and also the results are compared with the different methods. All of the numerical computations have been performed on a PC using several programs written in MAPLE 13.</div></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6324982">Cited in <strong>26</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A65R20" title="MSC2020">65R20</a> </td> <td class="space"> Numerical methods for integral equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A45F05" title="MSC2020">45F05</a> </td> <td class="space"> Systems of nonsingular linear integral equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A45G15" title="MSC2020">45G15</a> </td> <td class="space"> Systems of nonlinear integral equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A45D05" title="MSC2020">45D05</a> </td> <td class="space"> Volterra integral equations </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Asystem+of+Volterra+integral+equations">system of Volterra integral equations</a>; <a href="/?q=ut%3Aspectral+approximations">spectral approximations</a>; <a href="/?q=ut%3ALegendre+polynomials">Legendre polynomials</a>; <a href="/?q=ut%3AGauss+quadrature+rules">Gauss quadrature rules</a>; <a href="/?q=ut%3Anumerical+examples">numerical examples</a>; <a href="/?q=ut%3ALegendre-collocation+method">Legendre-collocation method</a>; <a href="/?q=ut%3Alinear">linear</a>; <a href="/?q=ut%3Anonlinear">nonlinear</a></div> <div class="software"> <h3>Software:</h3><a href="/software/545">Maple</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 1295.65128" data-ciurl="/ci/06324982" data-biburl="/bibtex/06324982.bib" data-amsurl="/amsrefs/06324982.bib" data-xmlurl="/xml/06324982.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06324982.pdf" title="Zbl 1295.65128 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/10.1007/s12190-012-0582-8" aria-label="DOI for “The spectral method for solving systems of Volterra integral equations”" title="10.1007/s12190-012-0582-8">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">Aminikhah, H., Biazar, J.: A new analytical method for solving systems of Volterra integral equations. 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