Document Zbl 1535.65309

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Numer. Math.</a> <a href="/?q=in%3A510557" title="Articles in this Issue">197, 243-257 (2024)</a>. </div> <div class="abstract">Summary: The paper addresses a computational method to simulate more accurate models for population growth with immigration, focusing on integral equations (IEs) featuring a delay parameter in the time variable. The proposed method utilizes Legendre wavelets within the Galerkin scheme as a orthonormal basis. Legendre wavelets are known for their localized functions, offering suitable precision and stability in simulating time-delay biological models. This approach employs the composite Gauss-Legendre (CGL) quadrature rule to compute integrals appeared in the scheme. An error bound analysis demonstrates a convergence rate of order $2^{- Mk}$. Additionally, various numerical examples are presented to show the efficiency, accuracy and validate the theoretical error estimate of the novel technique.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7827767">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%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%3A45G10" title="MSC2020">45G10</a> </td> <td class="space"> Other 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><tr> <td> <a class="mono" href="/classification/?q=cc%3A65T60" title="MSC2020">65T60</a> </td> <td class="space"> Numerical methods for wavelets </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Apopulation+model">population model</a>; <a href="/?q=ut%3Aimmigration">immigration</a>; <a href="/?q=ut%3Adelay+parameter">delay parameter</a>; <a href="/?q=ut%3Aintegral+equation">integral equation</a>; <a href="/?q=ut%3ALegendre+wavelets">Legendre wavelets</a>; <a href="/?q=ut%3AGalerkin+method">Galerkin method</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 1535.65309" data-ciurl="/ci/07827767" data-biburl="/bibtex/07827767.bib" data-amsurl="/amsrefs/07827767.bib" data-xmlurl="/xml/07827767.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07827767.pdf" title="Zbl 1535.65309 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.apnum.2023.11.018" aria-label="DOI for “The numerical solution of a time-delay model of population growth with immigration using Legendre wavelets”" title="10.1016/j.apnum.2023.11.018">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">Amin, R.; Shah, K.; Asif, M.; Khan, I., Efficient numerical technique for solution of delay Volterra-Fredholm integral equations using Haar wavelet. 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