Document Zbl 1295.35163

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Appl. Math. Comput.</a> <a href="/?q=in%3A334350" title="Articles in this Issue">43, No. 1-2, 31-54 (2013)</a>. </div> <div class="abstract">Summary: In this paper, we present a new approach to solve nonlocal initial-boundary value problems of linear and nonlinear hyperbolic partial differential equations of first-order subject to initial and nonlocal boundary conditions of integral type. We first transform the given nonlocal initial-boundary value problems into local initial-boundary value problems. Then we apply a modified Adomian decomposition method, which permits convenient resolution of these problems. Moreover, we prove this decomposition scheme applied to such nonlocal problems is convergent in a suitable Hilbert space, and then extend our discussion to include systems of first-order linear equations and other related nonlocal initial-boundary value problems.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6325266">Cited in <strong>2</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A35C05" title="MSC2020">35C05</a> </td> <td class="space"> Solutions to PDEs in closed form </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35L04" title="MSC2020">35L04</a> </td> <td class="space"> Initial-boundary value problems for first-order hyperbolic equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35L20" title="MSC2020">35L20</a> </td> <td class="space"> Initial-boundary value problems for second-order hyperbolic equations </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Asystems+of+first-order+hyperbolic+partial+differential+equations">systems of first-order hyperbolic partial differential equations</a>; <a href="/?q=ut%3AAdomian+decomposition+method">Adomian decomposition method</a>; <a href="/?q=ut%3AAdomian+polynomials">Adomian polynomials</a>; <a href="/?q=ut%3Anonlocal+boundary+conditions+of+integral+type">nonlocal boundary conditions of integral type</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 1295.35163" data-ciurl="/ci/06325266" data-biburl="/bibtex/06325266.bib" data-amsurl="/amsrefs/06325266.bib" data-xmlurl="/xml/06325266.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06325266.pdf" title="Zbl 1295.35163 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/s12190-013-0650-8" aria-label="DOI for “An efficient method for solving nonlocal initial-boundary value problems for linear and nonlinear first-order hyperbolic partial differential equations”" title="10.1007/s12190-013-0650-8">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">Cannon, J.R.: The solution of the heat equation subject to the specification of energy. 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