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equation</title> <meta name="description" content="Search results for: Pell's equation"> <meta name="keywords" content="Pell's equation"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> <button class="d-block d-lg-none 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action="https://publications.waset.org/search"> <div id="custom-search-input"> <div class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value="Pell's equation"> <input type="submit" class="btn_search" value="Search"> </div> </div> </form> </div> </div> <div class="row mt-3"> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Commenced</strong> in January 2007</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Frequency:</strong> Monthly</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Edition:</strong> International</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Paper Count:</strong> 1093</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: Pell's equation</h1> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1093</span> The Proof of Two Conjectures Related to Pell-s Equation x2 −Dy2 = ± 4</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Armend%20Sh.%20Shabani">Armend Sh. Shabani</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Let D ≠ 1 be a positive non-square integer. In this paper are given the proofs for two conjectures related to Pell-s equation x2 -Dy2 = ± 4, proposed by A. Tekcan. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Pell%27s%20equation" title="Pell's equation">Pell's equation</a>, <a href="https://publications.waset.org/search?q=solutions%20of%20Pell%27s%20equation." title=" solutions of Pell's equation."> solutions of Pell's equation.</a> </p> <a href="https://publications.waset.org/14954/the-proof-of-two-conjectures-related-to-pell-s-equation-x2-dy2-4" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/14954/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/14954/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/14954/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/14954/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/14954/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/14954/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/14954/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/14954/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/14954/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/14954/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/14954.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">1240</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">1092</span> The Pell Equation x2 − Py2 = Q</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Ahmet%20Tekcan">Ahmet Tekcan</a>, <a href="https://publications.waset.org/search?q=Arzu%20%C3%96zko%C3%A7"> Arzu Özkoç</a>, <a href="https://publications.waset.org/search?q=Canan%20Kocap%C4%B1nar"> Canan Kocapınar</a>, <a href="https://publications.waset.org/search?q=Hatice%20Alkan"> Hatice Alkan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Let p be a prime number such that p ≡ 1(mod 4), say p = 1+4k for a positive integer k. Let P = 2k + 1 and Q = k2. In this paper, we consider the integer solutions of the Pell equation x2-Py2 = Q over Z and also over finite fields Fp. Also we deduce some relations on the integer solutions (xn, yn) of it. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Pell%20equation" title="Pell equation">Pell equation</a>, <a href="https://publications.waset.org/search?q=solutions%20of%20Pell%20equation." title=" solutions of Pell equation."> solutions of Pell equation.</a> </p> <a href="https://publications.waset.org/7822/the-pell-equation-x2-py2-q" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/7822/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/7822/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/7822/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/7822/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/7822/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/7822/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/7822/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/7822/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/7822/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/7822/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/7822.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">2107</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">1091</span> On the Integer Solutions of the Pell Equation x2 - dy2 = 2t</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Ahmet%20Tekcan">Ahmet Tekcan</a>, <a href="https://publications.waset.org/search?q=Bet%C3%BCl%20Gezer"> Betül Gezer</a>, <a href="https://publications.waset.org/search?q=Osman%20Bizim"> Osman Bizim</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>Let k ≥ 1 and t ≥ 0 be two integers and let d = k2 + k be a positive non-square integer. In this paper, we consider the integer solutions of Pell equation x2 - dy2 = 2t. Further we derive a recurrence relation on the solutions of this equation.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Pell%20equation" title="Pell equation">Pell equation</a>, <a href="https://publications.waset.org/search?q=Diophantine%20equation." title=" Diophantine equation."> Diophantine equation.</a> </p> <a href="https://publications.waset.org/423/on-the-integer-solutions-of-the-pell-equation-x2-dy2-2t" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/423/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/423/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/423/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/423/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/423/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/423/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/423/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/423/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/423/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/423/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/423.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">2391</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">1090</span> The Pell Equation x2 − (k2 − k)y2 = 2t</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Ahmet%20Tekcan">Ahmet Tekcan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Let k, t, d be arbitrary integers with k ≥ 2, t ≥ 0 and d = k2 - k. In the first section we give some preliminaries from Pell equations x2 - dy2 = 1 and x2 - dy2 = N, where N be any fixed positive integer. In the second section, we consider the integer solutions of Pell equations x2 - dy2 = 1 and x2 - dy2 = 2t. We give a method for the solutions of these equations. Further we derive recurrence relations on the solutions of these equations <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Pell%20equation" title="Pell equation">Pell equation</a>, <a href="https://publications.waset.org/search?q=solutions%20of%20Pell%20equation." title=" solutions of Pell equation."> solutions of Pell equation.</a> </p> <a href="https://publications.waset.org/7073/the-pell-equation-x2-k2-ky2-2t" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/7073/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/7073/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/7073/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/7073/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/7073/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/7073/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/7073/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/7073/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/7073/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/7073/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/7073.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">1477</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">1089</span> The Diophantine Equation y2 − 2yx − 3 = 0 and Corresponding Curves over Fp</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Ahmet%20Tekcan">Ahmet Tekcan</a>, <a href="https://publications.waset.org/search?q=Arzu%20%C3%96zko%C3%A7"> Arzu Özkoç</a>, <a href="https://publications.waset.org/search?q=Hatice%20Alkan"> Hatice Alkan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work, we consider the number of integer solutions of Diophantine equation D : y2 - 2yx - 3 = 0 over Z and also over finite fields Fp for primes p ≥ 5. Later we determine the number of rational points on curves Ep : y2 = Pp(x) = yp 1 + yp 2 over Fp, where y1 and y2 are the roots of D. Also we give a formula for the sum of x- and y-coordinates of all rational points (x, y) on Ep over Fp. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Diophantine%20equation" title="Diophantine equation">Diophantine equation</a>, <a href="https://publications.waset.org/search?q=Pell%20equation" title=" Pell equation"> Pell equation</a>, <a href="https://publications.waset.org/search?q=quadratic%20form." title=" quadratic form."> quadratic form.</a> </p> <a href="https://publications.waset.org/6133/the-diophantine-equation-y2-2yx-3-0-and-corresponding-curves-over-fp" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/6133/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/6133/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/6133/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/6133/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/6133/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/6133/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/6133/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/6133/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/6133/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/6133/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/6133.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">1267</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">1088</span> A Special Algorithm to Approximate the Square Root of Positive Integer</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Hsian%20Ming%20Goo">Hsian Ming Goo</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>The paper concerns a special approximate algorithm of the square root of the specific positive integer, which is built by the use of the property of positive integer solution of the Pell’s equation, together with using some elementary theorems of matrices, and then takes it to compare with general used the Newton’s method and give a practical numerical example and error analysis; it is unexpected to find its special property: the significant figure of the approximation value of the square root of positive integer will increase one digit by one. It is well useful in some occasions.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Special%20approximate%20algorithm" title="Special approximate algorithm">Special approximate algorithm</a>, <a href="https://publications.waset.org/search?q=square%20root" title=" square root"> square root</a>, <a href="https://publications.waset.org/search?q=Pell%E2%80%99s%0D%0Aequation" title=" Pell’s equation"> Pell’s equation</a>, <a href="https://publications.waset.org/search?q=Newton%E2%80%99s%20method" title=" Newton’s method"> Newton’s method</a>, <a href="https://publications.waset.org/search?q=error%20analysis." title=" error analysis."> error analysis.</a> </p> <a href="https://publications.waset.org/16980/a-special-algorithm-to-approximate-the-square-root-of-positive-integer" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/16980/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/16980/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/16980/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/16980/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/16980/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/16980/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/16980/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/16980/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/16980/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/16980/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/16980.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">2803</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">1087</span> An Analytical Method for Solving General Riccati Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Y.%20Pala">Y. Pala</a>, <a href="https://publications.waset.org/search?q=M.%20O.%20Ertas"> M. O. Ertas</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, the general Riccati equation is analytically solved by a new transformation. By the method developed, looking at the transformed equation, whether or not an explicit solution can be obtained is readily determined. Since the present method does not require a proper solution for the general solution, it is especially suitable for equations whose proper solutions cannot be seen at first glance. Since the transformed second order linear equation obtained by the present transformation has the simplest form that it can have, it is immediately seen whether or not the original equation can be solved analytically. The present method is exemplified by several examples.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Riccati%20Equation" title="Riccati Equation">Riccati Equation</a>, <a href="https://publications.waset.org/search?q=ordinary%20differential%20equation" title=" ordinary differential equation"> ordinary differential equation</a>, <a href="https://publications.waset.org/search?q=nonlinear%20differential%20equation" title=" nonlinear differential equation"> nonlinear differential equation</a>, <a href="https://publications.waset.org/search?q=analytical%20solution" title=" analytical solution"> analytical solution</a>, <a href="https://publications.waset.org/search?q=proper%20solution." title=" proper solution."> proper solution.</a> </p> <a href="https://publications.waset.org/10006683/an-analytical-method-for-solving-general-riccati-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10006683/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10006683/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10006683/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10006683/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10006683/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10006683/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10006683/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10006683/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10006683/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10006683/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10006683.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">2025</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">1086</span> Solution of The KdV Equation with Asymptotic Degeneracy</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Tapas%20Kumar%20Sinha">Tapas Kumar Sinha</a>, <a href="https://publications.waset.org/search?q=Joseph%20Mathew"> Joseph Mathew</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>Recently T. C. Au-Yeung, C.Au, and P. C. W. Fung [2] have given the solution of the KdV equation [1] to the boundary condition , where b is a constant. We have further extended the method of [2] to find the solution of the KdV equation with asymptotic degeneracy. Via simulations we find both bright and dark Solitons (i.e. Solitons with opposite phases).</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=KdV%20equation" title="KdV equation">KdV equation</a>, <a href="https://publications.waset.org/search?q=Asymptotic%20Degeneracy" title=" Asymptotic Degeneracy"> Asymptotic Degeneracy</a>, <a href="https://publications.waset.org/search?q=Solitons" title=" Solitons"> Solitons</a>, <a href="https://publications.waset.org/search?q=Inverse%20Scattering" title=" Inverse Scattering"> Inverse Scattering</a> </p> <a href="https://publications.waset.org/1871/solution-of-the-kdv-equation-with-asymptotic-degeneracy" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/1871/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/1871/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/1871/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/1871/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/1871/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/1871/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/1871/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/1871/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/1871/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/1871/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/1871.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">1621</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">1085</span> Exact Solutions of the Helmholtz equation via the Nikiforov-Uvarov Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Said%20Laachir">Said Laachir</a>, <a href="https://publications.waset.org/search?q=Aziz%20Laaribi"> Aziz Laaribi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>The Helmholtz equation often arises in the study of physical problems involving partial differential equation. Many researchers have proposed numerous methods to find the analytic or approximate solutions for the proposed problems. In this work, the exact analytical solutions of the Helmholtz equation in spherical polar coordinates are presented using the Nikiforov-Uvarov (NU) method. It is found that the solution of the angular eigenfunction can be expressed by the associated-Legendre polynomial and radial eigenfunctions are obtained in terms of the Laguerre polynomials. The special case for k=0, which corresponds to the Laplace equation is also presented.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Helmholtz%20equation" title="Helmholtz equation">Helmholtz equation</a>, <a href="https://publications.waset.org/search?q=Nikiforov-Uvarov%20method" title=" Nikiforov-Uvarov method"> Nikiforov-Uvarov method</a>, <a href="https://publications.waset.org/search?q=exact%20solutions" title=" exact solutions"> exact solutions</a>, <a href="https://publications.waset.org/search?q=eigenfunctions." title=" eigenfunctions."> eigenfunctions.</a> </p> <a href="https://publications.waset.org/9996665/exact-solutions-of-the-helmholtz-equation-via-the-nikiforov-uvarov-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/9996665/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/9996665/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/9996665/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/9996665/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/9996665/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/9996665/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/9996665/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/9996665/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/9996665/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/9996665/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/9996665.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">3004</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">1084</span> Study of Cahn-Hilliard Equation to Simulate Phase Separation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Nara%20Guimar%C3%A3es">Nara Guimarães</a>, <a href="https://publications.waset.org/search?q=Marcelo%20Aquino%20Martorano"> Marcelo Aquino Martorano</a>, <a href="https://publications.waset.org/search?q=Douglas%20Gouv%C3%AAa"> Douglas Gouvêa</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>An investigation into Cahn-Hilliard equation was carried out through numerical simulation to identify a possible phase separation for one and two dimensional domains. It was observed that this equation can reproduce important mass fluxes necessary for phase separation within the miscibility gap and for coalescence of particles.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Cahn-Hilliard%20equation" title="Cahn-Hilliard equation">Cahn-Hilliard equation</a>, <a href="https://publications.waset.org/search?q=miscibility%20gap" title=" miscibility gap"> miscibility gap</a>, <a href="https://publications.waset.org/search?q=phase%0D%0Aseparation." title=" phase separation."> phase separation.</a> </p> <a href="https://publications.waset.org/10000644/study-of-cahn-hilliard-equation-to-simulate-phase-separation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10000644/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10000644/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10000644/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10000644/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10000644/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10000644/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10000644/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10000644/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10000644/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10000644/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10000644.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">2054</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">1083</span> Transient Population Dynamics of Phase Singularities in 2D Beeler-Reuter Model</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Hidetoshi%20Konno"> Hidetoshi Konno</a>, <a href="https://publications.waset.org/search?q=Akio%20Suzuki"> Akio Suzuki</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>The paper presented a transient population dynamics of phase singularities in 2D Beeler-Reuter model. Two stochastic modelings are examined: (i) the Master equation approach with the transition rate (i.e., λ(n, t) = λ(t)n and μ(n, t) = μ(t)n) and (ii) the nonlinear Langevin equation approach with a multiplicative noise. The exact general solution of the Master equation with arbitrary time-dependent transition rate is given. Then, the exact solution of the mean field equation for the nonlinear Langevin equation is also given. It is demonstrated that transient population dynamics is successfully identified by the generalized Logistic equation with fractional higher order nonlinear term. It is also demonstrated the necessity of introducing time-dependent transition rate in the master equation approach to incorporate the effect of nonlinearity.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Transient%20population%20dynamics" title=" Transient population dynamics"> Transient population dynamics</a>, <a href="https://publications.waset.org/search?q=Phase%20singularity" title=" Phase singularity"> Phase singularity</a>, <a href="https://publications.waset.org/search?q=Birth-death%20process" title=" Birth-death process"> Birth-death process</a>, <a href="https://publications.waset.org/search?q=Non-stationary%20Master%20equation" title=" Non-stationary Master equation"> Non-stationary Master equation</a>, <a href="https://publications.waset.org/search?q=nonlinear%20Langevin%20equation" title=" nonlinear Langevin equation"> nonlinear Langevin equation</a>, <a href="https://publications.waset.org/search?q=generalized%20Logistic%20equation." title=" generalized Logistic equation."> generalized Logistic equation.</a> </p> <a href="https://publications.waset.org/16095/transient-population-dynamics-of-phase-singularities-in-2d-beeler-reuter-model" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/16095/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/16095/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/16095/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/16095/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/16095/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/16095/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/16095/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/16095/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/16095/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/16095/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/16095.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">1594</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">1082</span> Traveling Wave Solutions for the Sawada-Kotera-Kadomtsev-Petviashivili Equation and the Bogoyavlensky-Konoplechenko Equation by (G'/G)- Expansion Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Nisha%20Goyal">Nisha Goyal</a>, <a href="https://publications.waset.org/search?q=R.K.%20Gupta"> R.K. Gupta</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>This paper presents a new function expansion method for finding traveling wave solutions of a nonlinear equations and calls it the G G -expansion method, given by Wang et al recently. As an application of this new method, we study the well-known Sawada-Kotera-Kadomtsev-Petviashivili equation and Bogoyavlensky-Konoplechenko equation. With two new expansions, general types of soliton solutions and periodic solutions for these two equations are obtained.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Sawada-Kotera-Kadomtsev-Petviashivili%20equation" title="Sawada-Kotera-Kadomtsev-Petviashivili equation">Sawada-Kotera-Kadomtsev-Petviashivili equation</a>, <a href="https://publications.waset.org/search?q=Bogoyavlensky-Konoplechenko%20equation" title=" Bogoyavlensky-Konoplechenko equation"> Bogoyavlensky-Konoplechenko equation</a>, <a href="https://publications.waset.org/search?q=" title=" "> </a> </p> <a href="https://publications.waset.org/15030/traveling-wave-solutions-for-the-sawada-kotera-kadomtsev-petviashivili-equation-and-the-bogoyavlensky-konoplechenko-equation-by-gg-expansion-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/15030/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/15030/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/15030/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/15030/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/15030/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/15030/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/15030/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/15030/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/15030/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/15030/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/15030.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">1618</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">1081</span> Stability of Fractional Differential Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Rabha%20W.%20Ibrahim">Rabha W. Ibrahim</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>We study a Dirichlet boundary value problem for Lane-Emden equation involving two fractional orders. Lane-Emden equation has been widely used to describe a variety of phenomena in physics and astrophysics, including aspects of stellar structure, the thermal history of a spherical cloud of gas, isothermal gas spheres,and thermionic currents. However, ordinary Lane-Emden equation does not provide the correct description of the dynamics for systems in complex media. In order to overcome this problem and describe dynamical processes in a fractalmedium, numerous generalizations of Lane-Emden equation have been proposed. One such generalization replaces the ordinary derivative by a fractional derivative in the Lane-Emden equation. This gives rise to the fractional Lane-Emden equation with a single index. Recently, a new type of Lane-Emden equation with two different fractional orders has been introduced which provides a more flexible model for fractal processes as compared with the usual one characterized by a single index. The contraction mapping principle and Krasnoselskiis fixed point theorem are applied to prove the existence of solutions of the problem in a Banach space. Ulam-Hyers stability for iterative Cauchy fractional differential equation is defined and studied.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Fractional%20calculus" title="Fractional calculus">Fractional calculus</a>, <a href="https://publications.waset.org/search?q=fractional%20differential%20equation" title=" fractional differential equation"> fractional differential equation</a>, <a href="https://publications.waset.org/search?q=Lane-Emden%20equation" title=" Lane-Emden equation"> Lane-Emden equation</a>, <a href="https://publications.waset.org/search?q=Riemann-Liouville%20fractional%20operators" title=" Riemann-Liouville fractional operators"> Riemann-Liouville fractional operators</a>, <a href="https://publications.waset.org/search?q=Volterra%20integral%20equation." title=" Volterra integral equation."> Volterra integral equation.</a> </p> <a href="https://publications.waset.org/16803/stability-of-fractional-differential-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/16803/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/16803/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/16803/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/16803/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/16803/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/16803/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/16803/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/16803/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/16803/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/16803/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/16803.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">3719</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">1080</span> Traveling Wave Solutions for Shallow Water Wave Equation by (G'/G)-Expansion Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Anjali%20Verma">Anjali Verma</a>, <a href="https://publications.waset.org/search?q=Ram%20Jiwari"> Ram Jiwari</a>, <a href="https://publications.waset.org/search?q=Jitender%20Kumar"> Jitender Kumar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>This paper presents a new function expansion method for finding traveling wave solution of a non-linear equation and calls it the (G'/G)-expansion method. The shallow water wave equation is reduced to a non linear ordinary differential equation by using a simple transformation. As a result the traveling wave solutions of shallow water wave equation are expressed in three forms: hyperbolic solutions, trigonometric solutions and rational solutions.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Shallow%20water%20wave%20equation" title="Shallow water wave equation">Shallow water wave equation</a>, <a href="https://publications.waset.org/search?q=Exact%20solutions" title=" Exact solutions"> Exact solutions</a>, <a href="https://publications.waset.org/search?q=%02%28G%27%2FG%29%20expansion%20method." title=" (G'/G) expansion method."> (G'/G) expansion method.</a> </p> <a href="https://publications.waset.org/16740/traveling-wave-solutions-for-shallow-water-wave-equation-by-gg-expansion-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/16740/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/16740/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/16740/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/16740/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/16740/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/16740/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/16740/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/16740/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/16740/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/16740/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/16740.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">1840</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">1079</span> Existence of Iterative Cauchy Fractional Differential Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Rabha%20W.%20Ibrahim">Rabha W. Ibrahim</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>Our main aim in this paper is to use the technique of non expansive operators to more general iterative and non iterative fractional differential equations (Cauchy type ). The non integer case is taken in sense of Riemann-Liouville fractional operators. Applications are illustrated.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Fractional%20calculus" title="Fractional calculus">Fractional calculus</a>, <a href="https://publications.waset.org/search?q=fractional%20differential%20equation" title=" fractional differential equation"> fractional differential equation</a>, <a href="https://publications.waset.org/search?q=Cauchy%20equation" title=" Cauchy equation"> Cauchy equation</a>, <a href="https://publications.waset.org/search?q=Riemann-Liouville%20fractional%20operators" title=" Riemann-Liouville fractional operators"> Riemann-Liouville fractional operators</a>, <a href="https://publications.waset.org/search?q=Volterra%0D%0Aintegral%20equation" title=" Volterra integral equation"> Volterra integral equation</a>, <a href="https://publications.waset.org/search?q=non-expansive%20mapping" title=" non-expansive mapping"> non-expansive mapping</a>, <a href="https://publications.waset.org/search?q=iterative%20differential%20equation." title=" iterative differential equation."> iterative differential equation.</a> </p> <a href="https://publications.waset.org/17037/existence-of-iterative-cauchy-fractional-differential-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/17037/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/17037/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/17037/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/17037/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/17037/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/17037/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/17037/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/17037/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/17037/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/17037/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/17037.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">2685</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">1078</span> Ginzburg-Landau Model for Curved Two-Phase Shallow Mixing Layers</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Irina%20Eglite">Irina Eglite</a>, <a href="https://publications.waset.org/search?q=Andrei%20A.%20Kolyshkin"> Andrei A. Kolyshkin</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Method of multiple scales is used in the paper in order to derive an amplitude evolution equation for the most unstable mode from two-dimensional shallow water equations under the rigid-lid assumption. It is assumed that shallow mixing layer is slightly curved in the longitudinal direction and contains small particles. Dynamic interaction between carrier fluid and particles is neglected. It is shown that the evolution equation is the complex Ginzburg-Landau equation. Explicit formulas for the computation of the coefficients of the equation are obtained. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Shallow%20water%20equations" title="Shallow water equations">Shallow water equations</a>, <a href="https://publications.waset.org/search?q=mixing%20layer" title=" mixing layer"> mixing layer</a>, <a href="https://publications.waset.org/search?q=weakly%0Anonlinear%20analysis" title=" weakly nonlinear analysis"> weakly nonlinear analysis</a>, <a href="https://publications.waset.org/search?q=Ginzburg-Landau%20equation" title=" Ginzburg-Landau equation"> Ginzburg-Landau equation</a> </p> <a href="https://publications.waset.org/14646/ginzburg-landau-model-for-curved-two-phase-shallow-mixing-layers" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/14646/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/14646/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/14646/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/14646/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/14646/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/14646/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/14646/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/14646/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/14646/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/14646/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/14646.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">1420</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">1077</span> Traveling Wave Solutions for the (3+1)-Dimensional Breaking Soliton Equation by (G'/G)- Expansion Method and Modified F-Expansion Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Mohammad%20Taghi%20Darvishi">Mohammad Taghi Darvishi</a>, <a href="https://publications.waset.org/search?q=Maliheh%20Najafi"> Maliheh Najafi</a>, <a href="https://publications.waset.org/search?q=Mohammad%20Najafi"> Mohammad Najafi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, using (G/G )-expansion method and modified F-expansion method, we give some explicit formulas of exact traveling wave solutions for the (3+1)-dimensional breaking soliton equation. A modified F-expansion method is proposed by taking full advantages of F-expansion method and Riccati equation in seeking exact solutions of the equation.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Exact%20solution" title="Exact solution">Exact solution</a>, <a href="https://publications.waset.org/search?q=The%20%283%2B1%29-dimensional%20breaking%20soliton%20equation" title=" The (3+1)-dimensional breaking soliton equation"> The (3+1)-dimensional breaking soliton equation</a>, <a href="https://publications.waset.org/search?q=%28%20G%20G%20%29-expansion%20method" title=" ( G G )-expansion method"> ( G G )-expansion method</a>, <a href="https://publications.waset.org/search?q=Riccati%20equation" title=" Riccati equation"> Riccati equation</a>, <a href="https://publications.waset.org/search?q=Modified%20Fexpansion%20method." title=" Modified Fexpansion method."> Modified Fexpansion method.</a> </p> <a href="https://publications.waset.org/12188/traveling-wave-solutions-for-the-31-dimensional-breaking-soliton-equation-by-gg-expansion-method-and-modified-f-expansion-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/12188/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/12188/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/12188/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/12188/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/12188/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/12188/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/12188/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/12188/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/12188/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/12188/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/12188.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">2725</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">1076</span> Lagrangian Method for Solving Unsteady Gas Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Amir%20Taghavi">Amir Taghavi</a>, <a href="https://publications.waset.org/search?q=kourosh%20Parand"> kourosh Parand</a>, <a href="https://publications.waset.org/search?q=Hosein%20Fani"> Hosein Fani</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper we propose, a Lagrangian method to solve unsteady gas equation which is a nonlinear ordinary differential equation on semi-infnite interval. This approach is based on Modified generalized Laguerre functions. This method reduces the solution of this problem to the solution of a system of algebraic equations. We also compare this work with some other numerical results. The findings show that the present solution is highly accurate.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Unsteady%20gas%20equation" title="Unsteady gas equation">Unsteady gas equation</a>, <a href="https://publications.waset.org/search?q=Generalized%20Laguerre%20functions" title=" Generalized Laguerre functions"> Generalized Laguerre functions</a>, <a href="https://publications.waset.org/search?q=Lagrangian%20method" title="Lagrangian method">Lagrangian method</a>, <a href="https://publications.waset.org/search?q=Nonlinear%20ODE." title=" Nonlinear ODE."> Nonlinear ODE.</a> </p> <a href="https://publications.waset.org/8328/lagrangian-method-for-solving-unsteady-gas-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/8328/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/8328/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/8328/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/8328/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/8328/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/8328/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/8328/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/8328/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/8328/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/8328/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/8328.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">1524</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">1075</span> Extend Three-wave Method for the (3+1)-Dimensional Soliton Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Somayeh%20Arbabi%20Mohammad-Abadi">Somayeh Arbabi Mohammad-Abadi</a>, <a href="https://publications.waset.org/search?q=Maliheh%20Najafi"> Maliheh Najafi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, we study (3+1)-dimensional Soliton equation. We employ the Hirota-s bilinear method to obtain the bilinear form of (3+1)-dimensional Soliton equation. Then by the idea of extended three-wave method, some exact soliton solutions including breather type solutions are presented.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Three-wave%20method" title="Three-wave method">Three-wave method</a>, <a href="https://publications.waset.org/search?q=%283%2B1%29-dimensional%20Soliton%20equation" title=" (3+1)-dimensional Soliton equation"> (3+1)-dimensional Soliton equation</a>, <a href="https://publications.waset.org/search?q=Hirota%27s%20bilinear%20form." title=" Hirota's bilinear form."> Hirota's bilinear form.</a> </p> <a href="https://publications.waset.org/9200/extend-three-wave-method-for-the-31-dimensional-soliton-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/9200/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/9200/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/9200/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/9200/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/9200/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/9200/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/9200/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/9200/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/9200/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/9200/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/9200.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">1560</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">1074</span> Parallel Algorithm for Numerical Solution of Three-Dimensional Poisson Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Alibek%20Issakhov">Alibek Issakhov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper developed and realized absolutely new algorithm for solving three-dimensional Poisson equation. This equation used in research of turbulent mixing, computational fluid dynamics, atmospheric front, and ocean flows and so on. Moreover in the view of rising productivity of difficult calculation there was applied the most up-to-date and the most effective parallel programming technology - MPI in combination with OpenMP direction, that allows to realize problems with very large data content. Resulted products can be used in solving of important applications and fundamental problems in mathematics and physics. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=MPI" title="MPI">MPI</a>, <a href="https://publications.waset.org/search?q=OpenMP" title=" OpenMP"> OpenMP</a>, <a href="https://publications.waset.org/search?q=three%20dimensional%20Poisson%20equation" title=" three dimensional Poisson equation"> three dimensional Poisson equation</a> </p> <a href="https://publications.waset.org/8613/parallel-algorithm-for-numerical-solution-of-three-dimensional-poisson-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/8613/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/8613/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/8613/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/8613/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/8613/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/8613/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/8613/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/8613/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/8613/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/8613/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/8613.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">1695</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">1073</span> Closed-Form Solution of Second Order Linear Ordinary Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Saeed%20Otarod">Saeed Otarod</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>A transformational method is employed to obtain closed-form integral solutions for nonhomogeneous second order linear ordinary differential equations in terms of a particular solution of the corresponding homogeneous part. To find the particular solution of the homogeneous part, the equation is first transformed into a simple Riccati equation from which the general solution of the nonhomogeneous second order linear differential equation, in the form of a closed integral equation, is inferred. The method is applied to the solution of Schr¨odinger equation for hydrogen-like atoms. A generic nonhomogeneous second order linear differential equation has also been solved to further exemplify the methodology.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Closed%20form" title="Closed form">Closed form</a>, <a href="https://publications.waset.org/search?q=Second%20order%20ordinary%20differential%20equations" title=" Second order ordinary differential equations"> Second order ordinary differential equations</a>, <a href="https://publications.waset.org/search?q=explicit" title=" explicit"> explicit</a>, <a href="https://publications.waset.org/search?q=linear%20equations" title=" linear equations"> linear equations</a>, <a href="https://publications.waset.org/search?q=differential%20equations." title=" differential equations."> differential equations.</a> </p> <a href="https://publications.waset.org/10013905/closed-form-solution-of-second-order-linear-ordinary-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10013905/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10013905/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10013905/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10013905/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10013905/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10013905/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10013905/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10013905/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10013905/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10013905/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10013905.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">8</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">1072</span> Iterative solutions to the linear matrix equation AXB + CXTD = E</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Yongxin%20Yuan">Yongxin Yuan</a>, <a href="https://publications.waset.org/search?q=Jiashang%20Jiang"> Jiashang Jiang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper the gradient based iterative algorithm is presented to solve the linear matrix equation AXB +CXTD = E, where X is unknown matrix, A,B,C,D,E are the given constant matrices. It is proved that if the equation has a solution, then the unique minimum norm solution can be obtained by choosing a special kind of initial matrices. Two numerical examples show that the introduced iterative algorithm is quite efficient. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=matrix%20equation" title="matrix equation">matrix equation</a>, <a href="https://publications.waset.org/search?q=iterative%20algorithm" title=" iterative algorithm"> iterative algorithm</a>, <a href="https://publications.waset.org/search?q=parameter%20estimation" title=" parameter estimation"> parameter estimation</a>, <a href="https://publications.waset.org/search?q=minimum%20norm%20solution." title="minimum norm solution.">minimum norm solution.</a> </p> <a href="https://publications.waset.org/12577/iterative-solutions-to-the-linear-matrix-equation-axb-cxtd-e" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/12577/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/12577/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/12577/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/12577/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/12577/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/12577/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/12577/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/12577/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/12577/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/12577/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/12577.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">1557</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">1071</span> Mechanical Equation of State in an Al-Li Alloy</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Jung-Ho%20Moon">Jung-Ho Moon</a>, <a href="https://publications.waset.org/search?q=Tae%20Kwon%20Ha"> Tae Kwon Ha</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>Existence of plastic equation of state has been investigated by performing a series of load relaxation tests at various temperatures using an Al-Li alloy. A plastic equation of state is first developed from a simple kinetics consideration for a mechanical activation process of a leading dislocation piled up against grain boundaries. A series of load relaxation test has been conducted at temperatures ranging from 200 to 530<sup>o</sup>C to obtain the stress-strain rate curves. A plastic equation of state has been derived from a simple consideration of dislocation kinetics and confirmed by experimental results.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Plastic%20equation%20of%20state" title="Plastic equation of state">Plastic equation of state</a>, <a href="https://publications.waset.org/search?q=Dislocation%20kinetics" title=" Dislocation kinetics"> Dislocation kinetics</a>, <a href="https://publications.waset.org/search?q=Load%20relaxation%20test" title=" Load relaxation test"> Load relaxation test</a>, <a href="https://publications.waset.org/search?q=Al-Li%20alloy" title=" Al-Li alloy"> Al-Li alloy</a>, <a href="https://publications.waset.org/search?q=Microstructure." title=" Microstructure."> Microstructure.</a> </p> <a href="https://publications.waset.org/17158/mechanical-equation-of-state-in-an-al-li-alloy" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/17158/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/17158/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/17158/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/17158/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/17158/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/17158/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/17158/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/17158/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/17158/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/17158/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/17158.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">1794</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">1070</span> Modification of Rk Equation of State for Liquid and Vapor of Ammonia by Genetic Algorithm</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=S.%20Mousavian">S. Mousavian</a>, <a href="https://publications.waset.org/search?q=F.%20Mousavian"> F. Mousavian</a>, <a href="https://publications.waset.org/search?q=V.%20Nikkhah%20Rashidabad"> V. Nikkhah Rashidabad</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>Cubic equations of state like Redlich–Kwong (RK)  EOS have been proved to be very reliable tools in the prediction of  phase behavior. Despite their good performance in compositional  calculations, they usually suffer from weaknesses in the predictions  of saturated liquid density. In this research, RK equation was  modified. The result of this study show that modified equation has  good agreement with experimental data.</p> <p> </p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Equation%20of%20state" title="Equation of state">Equation of state</a>, <a href="https://publications.waset.org/search?q=modification" title=" modification"> modification</a>, <a href="https://publications.waset.org/search?q=ammonia" title=" ammonia"> ammonia</a>, <a href="https://publications.waset.org/search?q=genetic%20algorithm." title=" genetic algorithm."> genetic algorithm.</a> </p> <a href="https://publications.waset.org/9997021/modification-of-rk-equation-of-state-for-liquid-and-vapor-of-ammonia-by-genetic-algorithm" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/9997021/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/9997021/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/9997021/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/9997021/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/9997021/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/9997021/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/9997021/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/9997021/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/9997021/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/9997021/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/9997021.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">2776</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">1069</span> The Splitting Upwind Schemes for Spectral Action Balance Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Anirut%20Luadsong">Anirut Luadsong</a>, <a href="https://publications.waset.org/search?q=Nitima%20Aschariyaphotha"> Nitima Aschariyaphotha</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The spectral action balance equation is an equation that used to simulate short-crested wind-generated waves in shallow water areas such as coastal regions and inland waters. This equation consists of two spatial dimensions, wave direction, and wave frequency which can be solved by finite difference method. When this equation with dominating convection term are discretized using central differences, stability problems occur when the grid spacing is chosen too coarse. In this paper, we introduce the splitting upwind schemes for avoiding stability problems and prove that it is consistent to the upwind scheme with same accuracy. The splitting upwind schemes was adopted to split the wave spectral action balance equation into four onedimensional problems, which for each small problem obtains the independently tridiagonal linear systems. For each smaller system can be solved by direct or iterative methods at the same time which is very fast when performed by a multi-processor computer. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=upwind%20scheme" title="upwind scheme">upwind scheme</a>, <a href="https://publications.waset.org/search?q=parallel%20algorithm" title=" parallel algorithm"> parallel algorithm</a>, <a href="https://publications.waset.org/search?q=spectral%20action%20balance%20equation" title=" spectral action balance equation"> spectral action balance equation</a>, <a href="https://publications.waset.org/search?q=splitting%20method." title=" splitting method."> splitting method.</a> </p> <a href="https://publications.waset.org/12679/the-splitting-upwind-schemes-for-spectral-action-balance-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/12679/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/12679/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/12679/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/12679/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/12679/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/12679/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/12679/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/12679/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/12679/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/12679/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/12679.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">1688</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">1068</span> Approximate Solution to Non-Linear Schrödinger Equation with Harmonic Oscillator by Elzaki Decomposition Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Emad%20K.%20Jaradat">Emad K. Jaradat</a>, <a href="https://publications.waset.org/search?q=Ala%E2%80%99a%20Al-Faqih"> Ala’a Al-Faqih</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>Nonlinear Schrödinger equations are regularly experienced in numerous parts of science and designing. Varieties of analytical methods have been proposed for solving these equations. In this work, we construct an approximate solution for the nonlinear Schrodinger equations, with harmonic oscillator potential, by Elzaki Decomposition Method (EDM). To illustrate the effects of harmonic oscillator on the behavior wave function, nonlinear Schrodinger equation in one and two dimensions is provided. The results show that, it is more perfectly convenient and easy to apply the EDM in one- and two-dimensional Schrodinger equation.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Non-linear%20Schrodinger%20equation" title="Non-linear Schrodinger equation">Non-linear Schrodinger equation</a>, <a href="https://publications.waset.org/search?q=Elzaki%20decomposition%20method" title=" Elzaki decomposition method"> Elzaki decomposition method</a>, <a href="https://publications.waset.org/search?q=harmonic%20oscillator" title=" harmonic oscillator"> harmonic oscillator</a>, <a href="https://publications.waset.org/search?q=one%20and%20two-%20dimensional%20Schrodinger%20equation." title=" one and two- dimensional Schrodinger equation. "> one and two- dimensional Schrodinger equation. </a> </p> <a href="https://publications.waset.org/10010018/approximate-solution-to-non-linear-schrodinger-equation-with-harmonic-oscillator-by-elzaki-decomposition-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10010018/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10010018/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10010018/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10010018/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10010018/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10010018/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10010018/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10010018/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10010018/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10010018/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10010018.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">906</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">1067</span> A Dynamic Equation for Downscaling Surface Air Temperature</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Ch.%20Surawut">Ch. Surawut</a>, <a href="https://publications.waset.org/search?q=D.%20Sukawat"> D. Sukawat</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In order to utilize results from global climate models, dynamical and statistical downscaling techniques have been developed. For dynamical downscaling, usually a limited area numerical model is used, with associated high computational cost. This research proposes dynamic equation for specific space-time regional climate downscaling from the Educational Global Climate Model (EdGCM) for Southeast Asia. The equation is for surface air temperature. This equation provides downscaling values of surface air temperature at any specific location and time without running a regional climate model. In the proposed equations, surface air temperature is approximated from ground temperature, sensible heat flux and 2m wind speed. Results from the application of the equation show that the errors from the proposed equations are less than the errors for direct interpolation from EdGCM. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Dynamic%20Equation" title="Dynamic Equation">Dynamic Equation</a>, <a href="https://publications.waset.org/search?q=Downscaling" title=" Downscaling"> Downscaling</a>, <a href="https://publications.waset.org/search?q=Inverse%20distance%0D%0Aweight%20interpolation." title=" Inverse distance weight interpolation."> Inverse distance weight interpolation.</a> </p> <a href="https://publications.waset.org/10003144/a-dynamic-equation-for-downscaling-surface-air-temperature" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10003144/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10003144/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10003144/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10003144/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10003144/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10003144/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10003144/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10003144/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10003144/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10003144/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10003144.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">2456</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">1066</span> Some Exact Solutions of the (2+1)-Dimensional Breaking Soliton Equation using the Three-wave Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Mohammad%20Taghi%20Darvishi">Mohammad Taghi Darvishi</a>, <a href="https://publications.waset.org/search?q=Mohammad%20Najafi"> Mohammad Najafi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>This paper considers the (2+1)-dimensional breaking soliton equation in its bilinear form. Some exact solutions to this equation are explicitly derived by the idea of three-wave solution method with the assistance of Maple. We can see that the new idea is very simple and straightforward.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Soliton%20solution" title="Soliton solution">Soliton solution</a>, <a href="https://publications.waset.org/search?q=computerized%20symbolic%20computation" title=" computerized symbolic computation"> computerized symbolic computation</a>, <a href="https://publications.waset.org/search?q=painleve%20analysis" title="painleve analysis">painleve analysis</a>, <a href="https://publications.waset.org/search?q=%282%2B1%29-dimensional%20breaking%20soliton%20equation" title=" (2+1)-dimensional breaking soliton equation"> (2+1)-dimensional breaking soliton equation</a>, <a href="https://publications.waset.org/search?q=Hirota%27s%20bilinear%20form." title=" Hirota's bilinear form."> Hirota's bilinear form.</a> </p> <a href="https://publications.waset.org/12525/some-exact-solutions-of-the-21-dimensional-breaking-soliton-equation-using-the-three-wave-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/12525/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/12525/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/12525/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/12525/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/12525/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/12525/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/12525/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/12525/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/12525/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/12525/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/12525.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">1910</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">1065</span> Septic B-spline Collocation Method for Solving One-dimensional Hyperbolic Telegraph Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Marzieh%20Dosti">Marzieh Dosti</a>, <a href="https://publications.waset.org/search?q=Alireza%20Nazemi"> Alireza Nazemi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>Recently, it is found that telegraph equation is more suitable than ordinary diffusion equation in modelling reaction diffusion for such branches of sciences. In this paper, a numerical solution for the one-dimensional hyperbolic telegraph equation by using the collocation method using the septic splines is proposed. The scheme works in a similar fashion as finite difference methods. Test problems are used to validate our scheme by calculate L2-norm and L∞-norm. The accuracy of the presented method is demonstrated by two test problems. The numerical results are found to be in good agreement with the exact solutions.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=B-spline" title="B-spline">B-spline</a>, <a href="https://publications.waset.org/search?q=collocation%20method" title=" collocation method"> collocation method</a>, <a href="https://publications.waset.org/search?q=second-order%20hyperbolic%20telegraph%20equation" title=" second-order hyperbolic telegraph equation"> second-order hyperbolic telegraph equation</a>, <a href="https://publications.waset.org/search?q=difference%20schemes." title=" difference schemes."> difference schemes.</a> </p> <a href="https://publications.waset.org/4298/septic-b-spline-collocation-method-for-solving-one-dimensional-hyperbolic-telegraph-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/4298/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/4298/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/4298/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/4298/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/4298/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/4298/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/4298/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/4298/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/4298/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/4298/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/4298.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">1797</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">1064</span> Heuristic Method for Judging the Computational Stability of the Difference Schemes of the Biharmonic Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Guang%20Zeng">Guang Zeng</a>, <a href="https://publications.waset.org/search?q=Jin%20Huang"> Jin Huang</a>, <a href="https://publications.waset.org/search?q=Zicai%20Li"> Zicai Li</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, we research the standard 13-point difference schemes for solving the biharmonic equation. Heuristic method is applied to judging the stability of multi-level difference schemes of the biharmonic equation. It is showed that the standard 13-point difference schemes are stable.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Finite-difference%20equation" title="Finite-difference equation">Finite-difference equation</a>, <a href="https://publications.waset.org/search?q=computational%20stability" title=" computational stability"> computational stability</a>, <a href="https://publications.waset.org/search?q=hirt%20method." title=" hirt method."> hirt method.</a> </p> <a href="https://publications.waset.org/1081/heuristic-method-for-judging-the-computational-stability-of-the-difference-schemes-of-the-biharmonic-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/1081/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/1081/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a 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