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Search results for: Blockpulse

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Blockpulse</h1> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2</span> Numerical Solution of Riccati Differential Equations by Using Hybrid Functions and Tau Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Changqing%20Yang">Changqing Yang</a>, <a href="https://publications.waset.org/search?q=Jianhua%20Hou"> Jianhua Hou</a>, <a href="https://publications.waset.org/search?q=Beibo%20Qin"> Beibo Qin</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>A numerical method for Riccati equation is presented in this work. The method is based on the replacement of unknown functions through a truncated series of hybrid of block-pulse functions and Chebyshev polynomials. The operational matrices of derivative and product of hybrid functions are presented. These matrices together with the tau method are then utilized to transform the differential equation into a system of algebraic equations. Corresponding numerical examples are presented to demonstrate the accuracy of the proposed method.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Hybrid%20functions" title="Hybrid functions">Hybrid functions</a>, <a href="https://publications.waset.org/search?q=Riccati%20differential%20equation" title=" Riccati differential equation"> Riccati differential equation</a>, <a href="https://publications.waset.org/search?q=Blockpulse" title=" Blockpulse"> Blockpulse</a>, <a href="https://publications.waset.org/search?q=Chebyshev%20polynomials" title=" Chebyshev polynomials"> Chebyshev polynomials</a>, <a href="https://publications.waset.org/search?q=Tau%20method" title=" Tau method"> Tau method</a>, <a href="https://publications.waset.org/search?q=operational%20matrix." title=" operational matrix."> operational matrix.</a> </p> <a href="https://publications.waset.org/7461/numerical-solution-of-riccati-differential-equations-by-using-hybrid-functions-and-tau-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/7461/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/7461/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/7461/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/7461/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/7461/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/7461/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/7461/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/7461/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/7461/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/7461/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/7461.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">2589</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1</span> Hybrid Function Method for Solving Nonlinear Fredholm Integral Equations of the Second Kind</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=jianhua%20Hou">jianhua Hou</a>, <a href="https://publications.waset.org/search?q=Changqing%20Yang">Changqing Yang</a>, <a href="https://publications.waset.org/search?q=and%20Beibo%20Qin">and Beibo Qin</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>A numerical method for solving nonlinear Fredholm integral equations of second kind is proposed. The Fredholm type equations which have many applications in mathematical physics are then considered. The method is based on hybrid function&nbsp; approximations. The properties of hybrid of block-pulse functions and Chebyshev polynomials are presented and are utilized to reduce the computation of nonlinear Fredholm integral equations to a system of nonlinear. Some numerical examples are selected to illustrate the effectiveness and simplicity of the method.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Hybrid%20functions" title="Hybrid functions">Hybrid functions</a>, <a href="https://publications.waset.org/search?q=Fredholm%20integral%20equation" title=" Fredholm integral equation"> Fredholm integral equation</a>, <a href="https://publications.waset.org/search?q=Blockpulse" title=" Blockpulse"> Blockpulse</a>, <a href="https://publications.waset.org/search?q=Chebyshev%20polynomials" title=" Chebyshev polynomials"> Chebyshev polynomials</a>, <a href="https://publications.waset.org/search?q=product%20operational%20matrix." title=" product operational matrix."> product operational matrix.</a> </p> <a href="https://publications.waset.org/16762/hybrid-function-method-for-solving-nonlinear-fredholm-integral-equations-of-the-second-kind" class="btn btn-primary btn-sm">Procedia</a> <a 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