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Benjamin-Bona-Mahony-Burgers equations</title> <meta name="description" content="Search results for: Benjamin-Bona-Mahony-Burgers equations"> <meta name="keywords" content="Benjamin-Bona-Mahony-Burgers equations"> <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 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style="font-size:1.6rem;">Search results for: Benjamin-Bona-Mahony-Burgers equations</h1> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1262</span> A Novel System of Two Coupled Equations for the Longitudinal Components of the Electromagnetic Field in a Waveguide</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Arti%20Vaish">Arti Vaish</a>, <a href="https://publications.waset.org/search?q=Harish%20Parthasarathy"> Harish Parthasarathy</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, a novel wave equation for electromagnetic waves in a medium having anisotropic permittivity has been derived with the help of Maxwell-s curl equations. The x and y components of the Maxwell-s equations are written with the permittivity () being a 3 × 3 symmetric matrix. These equations are solved for Ex , Ey, Hx, Hy in terms of Ez, Hz, and the partial derivatives. The Z components of the Maxwell-s curl are then used to arrive to the generalized Helmholtz equations for Ez and Hz. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Electromagnetism" title="Electromagnetism">Electromagnetism</a>, <a href="https://publications.waset.org/search?q=Maxwell%27s%20Equations" title=" Maxwell's Equations"> Maxwell's Equations</a>, <a href="https://publications.waset.org/search?q=Anisotropic%20permittivity" title=" Anisotropic permittivity"> Anisotropic permittivity</a>, <a href="https://publications.waset.org/search?q=Wave%20equation" title=" Wave equation"> Wave equation</a>, <a href="https://publications.waset.org/search?q=Matrix%20Equation" title=" Matrix Equation"> Matrix Equation</a>, <a href="https://publications.waset.org/search?q=Permittivity%20tensor." title=" Permittivity tensor."> Permittivity tensor.</a> </p> <a href="https://publications.waset.org/4089/a-novel-system-of-two-coupled-equations-for-the-longitudinal-components-of-the-electromagnetic-field-in-a-waveguide" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/4089/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/4089/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/4089/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/4089/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/4089/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/4089/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/4089/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/4089/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/4089/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/4089/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/4089.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">1702</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">1261</span> Application of the Hybrid Methods to Solving Volterra Integro-Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=G.Mehdiyeva">G.Mehdiyeva</a>, <a href="https://publications.waset.org/search?q=M.Imanova"> M.Imanova</a>, <a href="https://publications.waset.org/search?q=V.Ibrahimov"> V.Ibrahimov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Beginning from the creator of integro-differential equations Volterra, many scientists have investigated these equations. Classic method for solving integro-differential equations is the quadratures method that is successfully applied up today. Unlike these methods, Makroglou applied hybrid methods that are modified and generalized in this paper and applied to the numerical solution of Volterra integro-differential equations. The way for defining the coefficients of the suggested method is also given. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Integro-differential%20equations" title="Integro-differential equations">Integro-differential equations</a>, <a href="https://publications.waset.org/search?q=initial%20value%0Aproblem" title=" initial value problem"> initial value problem</a>, <a href="https://publications.waset.org/search?q=hybrid%20methods" title=" hybrid methods"> hybrid methods</a>, <a href="https://publications.waset.org/search?q=predictor-corrector%20method" title=" predictor-corrector method"> predictor-corrector method</a> </p> <a href="https://publications.waset.org/11196/application-of-the-hybrid-methods-to-solving-volterra-integro-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/11196/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/11196/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/11196/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/11196/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/11196/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/11196/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/11196/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/11196/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/11196/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/11196/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/11196.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">1732</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">1260</span> New Insight into Fluid Mechanics of Lorenz Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Yu-Kai%20Ting">Yu-Kai Ting</a>, <a href="https://publications.waset.org/search?q=Jia-Ying%20Tu"> Jia-Ying Tu</a>, <a href="https://publications.waset.org/search?q=Chung-Chun%20Hsiao"> Chung-Chun Hsiao</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>New physical insights into the nonlinear Lorenz equations related to flow resistance is discussed in this work. The chaotic dynamics related to Lorenz equations has been studied in many papers, which is due to the sensitivity of Lorenz equations to initial conditions and parameter uncertainties. However, the physical implication arising from Lorenz equations about convectional motion attracts little attention in the relevant literature. Therefore, as a first step to understand the related fluid mechanics of convectional motion, this paper derives the Lorenz equations again with different forced conditions in the model. Simulation work of the modified Lorenz equations without the viscosity or buoyancy force is discussed. The time-domain simulation results may imply that the states of the Lorenz equations are related to certain flow speed and flow resistance. The flow speed of the underlying fluid system increases as the flow resistance reduces. This observation would be helpful to analyze the coupling effects of different fluid parameters in a convectional model in future work.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Galerkin%20method" title="Galerkin method">Galerkin method</a>, <a href="https://publications.waset.org/search?q=Lorenz%20equations" title=" Lorenz equations"> Lorenz equations</a>, <a href="https://publications.waset.org/search?q=Navier-Stokes%0D%0Aequations." title=" Navier-Stokes equations."> Navier-Stokes equations.</a> </p> <a href="https://publications.waset.org/10000968/new-insight-into-fluid-mechanics-of-lorenz-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10000968/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10000968/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10000968/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10000968/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10000968/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10000968/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10000968/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10000968/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10000968/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10000968/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10000968.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">2310</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">1259</span> The Approximate Solution of Linear Fuzzy Fredholm Integral Equations of the Second Kind by Using Iterative Interpolation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=N.%20Parandin">N. Parandin</a>, <a href="https://publications.waset.org/search?q=M.%20A.%20Fariborzi%20Araghi"> M. A. Fariborzi Araghi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> in this paper, we propose a numerical method for the approximate solution of fuzzy Fredholm functional integral equations of the second kind by using an iterative interpolation. For this purpose, we convert the linear fuzzy Fredholm integral equations to a crisp linear system of integral equations. The proposed method is illustrated by some fuzzy integral equations in numerical examples. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Fuzzy%20function%20integral%20equations" title="Fuzzy function integral equations">Fuzzy function integral equations</a>, <a href="https://publications.waset.org/search?q=Iterative%20method" title=" Iterative method"> Iterative method</a>, <a href="https://publications.waset.org/search?q=Linear%20systems" title=" Linear systems"> Linear systems</a>, <a href="https://publications.waset.org/search?q=Parametric%20form%20of%20fuzzy%20number." title=" Parametric form of fuzzy number."> Parametric form of fuzzy number.</a> </p> <a href="https://publications.waset.org/12961/the-approximate-solution-of-linear-fuzzy-fredholm-integral-equations-of-the-second-kind-by-using-iterative-interpolation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/12961/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/12961/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/12961/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/12961/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/12961/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/12961/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/12961/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/12961/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/12961/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/12961/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/12961.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">1407</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">1258</span> A First Course in Numerical Methods with “Mathematica“</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Andrei%20A.%20Kolyshkin">Andrei A. Kolyshkin</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In the present paper some recommendations for the use of software package “Mathematica" in a basic numerical analysis course are presented. The methods which are covered in the course include solution of systems of linear equations, nonlinear equations and systems of nonlinear equations, numerical integration, interpolation and solution of ordinary differential equations. A set of individual assignments developed for the course covering all the topics is discussed in detail. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Numerical%20methods" title="Numerical methods">Numerical methods</a>, <a href="https://publications.waset.org/search?q=%22Mathematica%22" title=" "Mathematica""> "Mathematica"</a>, <a href="https://publications.waset.org/search?q=e-learning." title=" e-learning."> e-learning.</a> </p> <a href="https://publications.waset.org/2466/a-first-course-in-numerical-methods-with-mathematica" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/2466/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/2466/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/2466/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/2466/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/2466/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/2466/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/2466/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/2466/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/2466/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/2466/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/2466.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">3670</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">1257</span> An Efficient Computational Algorithm for Solving the Nonlinear Lane-Emden Type Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Gholamreza%20Hojjati">Gholamreza Hojjati</a>, <a href="https://publications.waset.org/search?q=Kourosh%20Parand"> Kourosh Parand</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper we propose a class of second derivative multistep methods for solving some well-known classes of Lane- Emden type equations which are nonlinear ordinary differential equations on the semi-infinite domain. These methods, which have good stability and accuracy properties, are useful in deal with stiff ODEs. We show superiority of these methods by applying them on the some famous Lane-Emden type equations.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Lane-Emden%20type%20equations" title="Lane-Emden type equations">Lane-Emden type equations</a>, <a href="https://publications.waset.org/search?q=nonlinear%20ODE" title=" nonlinear ODE"> nonlinear ODE</a>, <a href="https://publications.waset.org/search?q=stiff%20problems" title=" stiff problems"> stiff problems</a>, <a href="https://publications.waset.org/search?q=multistep%20methods" title=" multistep methods"> multistep methods</a>, <a href="https://publications.waset.org/search?q=astrophysics." title=" astrophysics."> astrophysics.</a> </p> <a href="https://publications.waset.org/11056/an-efficient-computational-algorithm-for-solving-the-nonlinear-lane-emden-type-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/11056/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/11056/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/11056/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/11056/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/11056/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/11056/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/11056/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/11056/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/11056/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/11056/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/11056.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">3180</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">1256</span> Equations of Pulse Propagation in Three-Layer Structure of As2S3 Chalcogenide Plasmonic Nano-Waveguides</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Leila%20Motamed-Jahromi">Leila Motamed-Jahromi</a>, <a href="https://publications.waset.org/search?q=Mohsen%20Hatami"> Mohsen Hatami</a>, <a href="https://publications.waset.org/search?q=Alireza%20Keshavarz"> Alireza Keshavarz </a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>This research aims at obtaining the equations of pulse propagation in nonlinear plasmonic waveguides created with As<sub>2</sub>S<sub>3</sub> chalcogenide materials. Via utilizing Helmholtz equation and first-order perturbation theory, two components of electric field are determined within frequency domain. Afterwards, the equations are formulated in time domain. The obtained equations include two coupled differential equations that considers nonlinear dispersion<span dir="RTL">.</span></p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Nonlinear%20optics" title="Nonlinear optics">Nonlinear optics</a>, <a href="https://publications.waset.org/search?q=propagation%20equation" title=" propagation equation"> propagation equation</a>, <a href="https://publications.waset.org/search?q=plasmonic%20waveguide." title=" plasmonic waveguide."> plasmonic waveguide.</a> </p> <a href="https://publications.waset.org/10005672/equations-of-pulse-propagation-in-three-layer-structure-of-as2s3-chalcogenide-plasmonic-nano-waveguides" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10005672/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10005672/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10005672/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10005672/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10005672/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10005672/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10005672/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10005672/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10005672/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10005672/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10005672.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">1299</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">1255</span> Development of Extended Trapezoidal Method for Numerical Solution of Volterra Integro-Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Fuziyah%20Ishak">Fuziyah Ishak</a>, <a href="https://publications.waset.org/search?q=Siti%20Norazura%20Ahmad"> Siti Norazura Ahmad</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>Volterra integro-differential equations appear in many models for real life phenomena. Since analytical solutions for this type of differential equations are hard and at times impossible to attain, engineers and scientists resort to numerical solutions that can be made as accurately as possible. Conventionally, numerical methods for ordinary differential equations are adapted to solve Volterra integro-differential equations. In this paper, numerical solution for solving Volterra integro-differential equation using extended trapezoidal method is described. Formulae for the integral and differential parts of the equation are presented. Numerical results show that the extended method is suitable for solving first order Volterra integro-differential equations.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Accuracy" title="Accuracy">Accuracy</a>, <a href="https://publications.waset.org/search?q=extended%20trapezoidal%20method" title=" extended trapezoidal method"> extended trapezoidal method</a>, <a href="https://publications.waset.org/search?q=numerical%20solution" title=" numerical solution"> numerical solution</a>, <a href="https://publications.waset.org/search?q=Volterra%20integro-differential%20equations." title=" Volterra integro-differential equations. "> Volterra integro-differential equations. </a> </p> <a href="https://publications.waset.org/10005777/development-of-extended-trapezoidal-method-for-numerical-solution-of-volterra-integro-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10005777/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10005777/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10005777/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10005777/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10005777/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10005777/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10005777/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10005777/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10005777/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10005777/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10005777.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">1656</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">1254</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">1475</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">1253</span> The Euler Equations of Steady Flow in Terms of New Dependent and Independent Variables</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Peiangpob%20Monnuanprang">Peiangpob Monnuanprang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper we study the transformation of Euler equations  1 , u u u Pf t (ρ ∂) + ⋅∇ = − ∇ + ∂ G G G G ∇⋅ = u 0, G where (ux, t) G G is the velocity of a fluid, P(x, t) G is the pressure of a fluid andρ (x, t) G is density. First of all, we rewrite the Euler equations in terms of new unknown functions. Then, we introduce new independent variables and transform it to a new curvilinear coordinate system. We obtain the Euler equations in the new dependent and independent variables. The governing equations into two subsystems, one is hyperbolic and another is elliptic.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Euler%20equations" title="Euler equations">Euler equations</a>, <a href="https://publications.waset.org/search?q=transformation" title=" transformation"> transformation</a>, <a href="https://publications.waset.org/search?q=hyperbolic" title=" hyperbolic"> hyperbolic</a>, <a href="https://publications.waset.org/search?q=elliptic" title=" elliptic"> elliptic</a> </p> <a href="https://publications.waset.org/7843/the-euler-equations-of-steady-flow-in-terms-of-new-dependent-and-independent-variables" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/7843/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/7843/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/7843/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/7843/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/7843/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/7843/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/7843/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/7843/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/7843/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/7843/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/7843.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">1737</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">1252</span> Automatic Iterative Methods for the Multivariate Solution of Nonlinear Algebraic Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Rafat%20Alshorman">Rafat Alshorman</a>, <a href="https://publications.waset.org/search?q=Safwan%20Al-Shara%27"> Safwan Al-Shara'</a>, <a href="https://publications.waset.org/search?q=I.%20Obeidat"> I. Obeidat</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Most real world systems express themselves formally as a set of nonlinear algebraic equations. As applications grow, the size and complexity of these equations also increase. In this work, we highlight the key concepts in using the homotopy analysis method as a methodology used to construct efficient iteration formulas for nonlinear equations solving. The proposed method is experimentally characterized according to a set of determined parameters which affect the systems. The experimental results show the potential and limitations of the new method and imply directions for future work. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Nonlinear%20Algebraic%20Equations" title="Nonlinear Algebraic Equations">Nonlinear Algebraic Equations</a>, <a href="https://publications.waset.org/search?q=Iterative%20Methods" title=" Iterative Methods"> Iterative Methods</a>, <a href="https://publications.waset.org/search?q=Homotopy%0AAnalysis%20Method." title=" Homotopy Analysis Method."> Homotopy Analysis Method.</a> </p> <a href="https://publications.waset.org/1301/automatic-iterative-methods-for-the-multivariate-solution-of-nonlinear-algebraic-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/1301/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/1301/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/1301/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/1301/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/1301/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/1301/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/1301/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/1301/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/1301/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/1301/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/1301.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">1912</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">1251</span> A New Approach to the Approximate Solutions of Hamilton-Jacobi Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Joe%20Imae">Joe Imae</a>, <a href="https://publications.waset.org/search?q=Kenjiro%20Shinagawa"> Kenjiro Shinagawa</a>, <a href="https://publications.waset.org/search?q=Tomoaki%20Kobayashi"> Tomoaki Kobayashi</a>, <a href="https://publications.waset.org/search?q=Guisheng%20Zhai"> Guisheng Zhai</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>We propose a new approach on how to obtain the approximate solutions of Hamilton-Jacobi (HJ) equations. The process of the approximation consists of two steps. The first step is to transform the HJ equations into the virtual time based HJ equations (VT-HJ) by introducing a new idea of ‘virtual-time’. The second step is to construct the approximate solutions of the HJ equations through a computationally iterative procedure based on the VT-HJ equations. It should be noted that the approximate feedback solutions evolve by themselves as the virtual-time goes by. Finally, we demonstrate the effectiveness of our approximation approach by means of simulations with linear and nonlinear control problems.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Nonlinear%20Control" title="Nonlinear Control">Nonlinear Control</a>, <a href="https://publications.waset.org/search?q=Optimal%20Control" title=" Optimal Control"> Optimal Control</a>, <a href="https://publications.waset.org/search?q=Hamilton-Jacobi%20Equation" title=" Hamilton-Jacobi Equation"> Hamilton-Jacobi Equation</a>, <a href="https://publications.waset.org/search?q=Virtual-Time" title=" Virtual-Time"> Virtual-Time</a> </p> <a href="https://publications.waset.org/14467/a-new-approach-to-the-approximate-solutions-of-hamilton-jacobi-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/14467/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/14467/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/14467/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/14467/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/14467/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/14467/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/14467/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/14467/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/14467/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/14467/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/14467.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">1512</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">1250</span> Integrable Heisenberg Ferromagnet Equations with Self-Consistent Potentials</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Gulgassyl%20Nugmanova">Gulgassyl Nugmanova</a>, <a href="https://publications.waset.org/search?q=Zhanat%20Zhunussova"> Zhanat Zhunussova</a>, <a href="https://publications.waset.org/search?q=Kuralay%20Yesmakhanova"> Kuralay Yesmakhanova</a>, <a href="https://publications.waset.org/search?q=Galya%20Mamyrbekova"> Galya Mamyrbekova</a>, <a href="https://publications.waset.org/search?q=Ratbay%20Myrzakulov"> Ratbay Myrzakulov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we consider some integrable Heisenberg Ferromagnet Equations with self-consistent potentials. We study their Lax representations. In particular we derive their equivalent counterparts in the form of nonlinear Schr¨odinger type equations. We present the integrable reductions of the Heisenberg Ferromagnet Equations with self-consistent potentials. These integrable Heisenberg Ferromagnet Equations with self-consistent potentials describe nonlinear waves in ferromagnets with some additional physical fields. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Spin%20systems" title="Spin systems">Spin systems</a>, <a href="https://publications.waset.org/search?q=equivalent%20counterparts" title=" equivalent counterparts"> equivalent counterparts</a>, <a href="https://publications.waset.org/search?q=integrable%0D%0Areductions" title=" integrable reductions"> integrable reductions</a>, <a href="https://publications.waset.org/search?q=self-consistent%20potentials." title=" self-consistent potentials."> self-consistent potentials.</a> </p> <a href="https://publications.waset.org/10002081/integrable-heisenberg-ferromagnet-equations-with-self-consistent-potentials" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10002081/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10002081/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10002081/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10002081/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10002081/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10002081/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10002081/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10002081/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10002081/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10002081/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10002081.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">1732</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">1249</span> Exp-Function Method for Finding Some Exact Solutions of Rosenau Kawahara and Rosenau Korteweg-de Vries Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Ehsan%20Mahdavi">Ehsan Mahdavi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, we apply the Exp-function method to Rosenau-Kawahara and Rosenau-KdV equations. Rosenau-Kawahara equation is the combination of the Rosenau and standard Kawahara equations and Rosenau-KdV equation is the combination of the Rosenau and standard KdV equations. These equations are nonlinear partial differential equations (NPDE) which play an important role in mathematical physics. Exp-function method is easy, succinct and powerful to implement to nonlinear partial differential equations arising in mathematical physics. We mainly try to present an application of Exp-function method and offer solutions for common errors wich occur during some of the recent works.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Exp-function%20method" title="Exp-function method">Exp-function method</a>, <a href="https://publications.waset.org/search?q=Rosenau%20Kawahara%20equation" title=" Rosenau Kawahara equation"> Rosenau Kawahara equation</a>, <a href="https://publications.waset.org/search?q=Rosenau%20Korteweg-de%20Vries%20equation" title=" Rosenau Korteweg-de Vries equation"> Rosenau Korteweg-de Vries equation</a>, <a href="https://publications.waset.org/search?q=nonlinear%20partial%20differential%0D%0Aequation." title=" nonlinear partial differential equation."> nonlinear partial differential equation.</a> </p> <a href="https://publications.waset.org/9999253/exp-function-method-for-finding-some-exact-solutions-of-rosenau-kawahara-and-rosenau-korteweg-de-vries-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/9999253/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/9999253/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/9999253/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/9999253/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/9999253/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/9999253/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/9999253/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/9999253/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/9999253/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/9999253/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/9999253.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">2058</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">1248</span> On Deterministic Chaos: Disclosing the Missing Mathematics from the Lorenz-Haken Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Belkacem%20Meziane">Belkacem Meziane</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>The original 3D Lorenz-Haken equations -which describe laser dynamics- are converted into 2-second-order differential equations out of which the so far missing mathematics is extracted. Leaning on high-order trigonometry, important outcomes are pulled out: A fundamental result attributes chaos to forbidden periodic solutions, inside some precisely delimited region of the control parameter space that governs self-pulsing.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=chaos" title="chaos">chaos</a>, <a href="https://publications.waset.org/search?q=Lorenz-Haken%20equations" title=" Lorenz-Haken equations"> Lorenz-Haken equations</a>, <a href="https://publications.waset.org/search?q=laser%20dynamics" title=" laser dynamics"> laser dynamics</a>, <a href="https://publications.waset.org/search?q=nonlinearities" title=" nonlinearities"> nonlinearities</a> </p> <a href="https://publications.waset.org/10012388/on-deterministic-chaos-disclosing-the-missing-mathematics-from-the-lorenz-haken-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10012388/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10012388/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10012388/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10012388/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10012388/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10012388/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10012388/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10012388/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10012388/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10012388/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10012388.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">610</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">1247</span> Numerical Solution for Integro-Differential Equations by Using Quartic B-Spline Wavelet and Operational Matrices</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Khosrow%20Maleknejad">Khosrow Maleknejad</a>, <a href="https://publications.waset.org/search?q=Yaser%20Rostami"> Yaser Rostami</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, Semi-orthogonal B-spline scaling functions and wavelets and their dual functions are presented to approximate the solutions of integro-differential equations.The B-spline scaling functions and wavelets, their properties and the operational matrices of derivative for this function are presented to reduce the solution of integro-differential equations to the solution of algebraic equations. Here we compute B-spline scaling functions of degree 4 and their dual, then we will show that by using them we have better approximation results for the solution of integro-differential equations in comparison with less degrees of scaling functions</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Integro-differential%20equations" title="Integro-differential equations">Integro-differential equations</a>, <a href="https://publications.waset.org/search?q=Quartic%20B-spline%0D%0Awavelet" title=" Quartic B-spline wavelet"> Quartic B-spline wavelet</a>, <a href="https://publications.waset.org/search?q=Operational%20matrices." title=" Operational matrices."> Operational matrices.</a> </p> <a href="https://publications.waset.org/9998762/numerical-solution-for-integro-differential-equations-by-using-quartic-b-spline-wavelet-and-operational-matrices" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/9998762/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/9998762/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/9998762/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/9998762/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/9998762/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/9998762/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/9998762/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/9998762/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/9998762/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/9998762/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/9998762.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">3151</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">1246</span> Strict Stability of Fuzzy Differential Equations with Impulse Effect</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Sanjay%20K.Srivastava">Sanjay K.Srivastava</a>, <a href="https://publications.waset.org/search?q=Bhanu%20Gupta"> Bhanu Gupta</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper some results on strict stability heve beeb extended for fuzzy differential equations with impulse effect using Lyapunov functions and Razumikhin technique.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Fuzzy%20differential%20equations" title="Fuzzy differential equations">Fuzzy differential equations</a>, <a href="https://publications.waset.org/search?q=Impulsive%20differential%20equations" title=" Impulsive differential equations"> Impulsive differential equations</a>, <a href="https://publications.waset.org/search?q=Strict%20stability" title=" Strict stability"> Strict stability</a>, <a href="https://publications.waset.org/search?q=Lyapunov%20function" title=" Lyapunov function"> Lyapunov function</a>, <a href="https://publications.waset.org/search?q=Razumikhin%20technique." title=" Razumikhin technique."> Razumikhin technique.</a> </p> <a href="https://publications.waset.org/16748/strict-stability-of-fuzzy-differential-equations-with-impulse-effect" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/16748/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/16748/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/16748/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/16748/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/16748/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/16748/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/16748/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/16748/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/16748/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/16748/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/16748.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">1469</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">1245</span> Toward a New Simple Analytical Formulation of Navier-Stokes Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Gunawan%20Nugroho">Gunawan Nugroho</a>, <a href="https://publications.waset.org/search?q=Ahmed%20M.%20S.%20Ali"> Ahmed M. S. Ali</a>, <a href="https://publications.waset.org/search?q=Zainal%20A.%20Abdul%20Karim"> Zainal A. Abdul Karim</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Incompressible Navier-Stokes equations are reviewed in this work. Three-dimensional Navier-Stokes equations are solved analytically. The Mathematical derivation shows that the solutions for the zero and constant pressure gradients are similar. Descriptions of the proposed formulation and validation against two laminar experiments and three different turbulent flow cases are reported in this paper. Even though, the analytical solution is derived for nonreacting flows, it could reproduce trends for cases including combustion. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Navier-Stokes%20Equations" title="Navier-Stokes Equations">Navier-Stokes Equations</a>, <a href="https://publications.waset.org/search?q=potential%20function" title=" potential function"> potential function</a>, <a href="https://publications.waset.org/search?q=turbulent%20flows." title=" turbulent flows."> turbulent flows.</a> </p> <a href="https://publications.waset.org/6484/toward-a-new-simple-analytical-formulation-of-navier-stokes-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/6484/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/6484/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/6484/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/6484/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/6484/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/6484/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/6484/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/6484/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/6484/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/6484/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/6484.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">2140</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">1244</span> Solving Linear Matrix Equations by Matrix Decompositions</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=Kezheng%20Zuo"> Kezheng Zuo</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, a system of linear matrix equations is considered. A new necessary and sufficient condition for the consistency of the equations is derived by means of the generalized singular-value decomposition, and the explicit representation of the general solution is provided.</p> <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=Generalized%20inverse" title=" Generalized inverse"> Generalized inverse</a>, <a href="https://publications.waset.org/search?q=Generalized%0D%0Asingular-value%20decomposition." title=" Generalized singular-value decomposition."> Generalized singular-value decomposition.</a> </p> <a href="https://publications.waset.org/10000378/solving-linear-matrix-equations-by-matrix-decompositions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10000378/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10000378/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10000378/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10000378/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10000378/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10000378/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10000378/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10000378/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10000378/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10000378/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10000378.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">2058</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">1243</span> Laplace Technique to Find General Solution of Differential Equations without Initial Conditions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Adil%20Al-Rammahi">Adil Al-Rammahi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>Laplace transformations have wide applications in engineering and sciences. All previous studies of modified Laplace transformations depend on differential equation with initial conditions. The purpose of our paper is to solve the linear differential equations (not initial value problem) and then find the general solution (not particular) via the Laplace transformations without needed any initial condition. The study involves both types of differential equations, ordinary and partial.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Differential%20Equations" title="Differential Equations">Differential Equations</a>, <a href="https://publications.waset.org/search?q=Laplace%20Transformations." title=" Laplace Transformations."> Laplace Transformations.</a> </p> <a href="https://publications.waset.org/10000213/laplace-technique-to-find-general-solution-of-differential-equations-without-initial-conditions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10000213/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10000213/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10000213/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10000213/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10000213/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10000213/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10000213/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10000213/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10000213/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10000213/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10000213.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">3184</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">1242</span> New Application of EHTA for the Generalized(2+1)-Dimensional Nonlinear Evolution Equations</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, the generalized (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff (shortly CBS) equations are investigated. We employ the Hirota-s bilinear method to obtain the bilinear form of CBS equations. Then by the idea of extended homoclinic test approach (shortly EHTA), 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=EHTA" title="EHTA">EHTA</a>, <a href="https://publications.waset.org/search?q=%282%2B1%29-dimensional%20CBS%20equations" title=" (2+1)-dimensional CBS equations"> (2+1)-dimensional CBS equations</a>, <a href="https://publications.waset.org/search?q=%282%2B1%29-dimensional%20breaking%20solution%20equation" title=" (2+1)-dimensional breaking solution equation"> (2+1)-dimensional breaking solution 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/13986/new-application-of-ehta-for-the-generalized21-dimensional-nonlinear-evolution-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/13986/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/13986/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/13986/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/13986/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/13986/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/13986/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/13986/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/13986/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/13986/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/13986/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/13986.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">1488</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">1241</span> Bifurcation Method for Solving Positive Solutions to a Class of Semilinear Elliptic Equations and Stability Analysis of Solutions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Hailong%20Zhu">Hailong Zhu</a>, <a href="https://publications.waset.org/search?q=Zhaoxiang%20Li"> Zhaoxiang Li</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>Semilinear elliptic equations are ubiquitous in natural sciences. They give rise to a variety of important phenomena in quantum mechanics, nonlinear optics, astrophysics, etc because they have rich multiple solutions. But the nontrivial solutions of semilinear equations are hard to be solved for the lack of stabilities, such as Lane-Emden equation, Henon equation and Chandrasekhar equation. In this paper, bifurcation method is applied to solving semilinear elliptic equations which are with homogeneous Dirichlet boundary conditions in 2D. Using this method, nontrivial numerical solutions will be computed and visualized in many different domains (such as square, disk, annulus, dumbbell, etc).</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Semilinear%20elliptic%20equations" title="Semilinear elliptic equations">Semilinear elliptic equations</a>, <a href="https://publications.waset.org/search?q=positive%20solutions" title=" positive solutions"> positive solutions</a>, <a href="https://publications.waset.org/search?q=bifurcation%20method" title=" bifurcation method"> bifurcation method</a>, <a href="https://publications.waset.org/search?q=isotropy%20subgroups." title=" isotropy subgroups."> isotropy subgroups.</a> </p> <a href="https://publications.waset.org/9287/bifurcation-method-for-solving-positive-solutions-to-a-class-of-semilinear-elliptic-equations-and-stability-analysis-of-solutions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/9287/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/9287/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/9287/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/9287/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/9287/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/9287/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/9287/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/9287/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/9287/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/9287/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/9287.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">1648</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">1240</span> Numerical Solution of Hammerstein Integral Equations by Using Quasi-Interpolation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=M.%20Zarebnia">M. Zarebnia</a>, <a href="https://publications.waset.org/search?q=S.%20Khani"> S. Khani</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper first, a numerical method based on quasiinterpolation for solving nonlinear Fredholm integral equations of the Hammerstein-type is presented. Then, we approximate the solution of Hammerstein integral equations by Nystrom’s method. Also, we compare the methods with some numerical examples.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Hammerstein%20integral%20equations" title="Hammerstein integral equations">Hammerstein integral equations</a>, <a href="https://publications.waset.org/search?q=quasi-interpolation" title=" quasi-interpolation"> quasi-interpolation</a>, <a href="https://publications.waset.org/search?q=Nystrom%E2%80%99s%20method." title=" Nystrom’s method."> Nystrom’s method.</a> </p> <a href="https://publications.waset.org/16795/numerical-solution-of-hammerstein-integral-equations-by-using-quasi-interpolation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/16795/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/16795/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/16795/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/16795/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/16795/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/16795/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/16795/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/16795/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/16795/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/16795/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/16795.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">4472</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">1239</span> A Modification on Newton's Method for Solving Systems of Nonlinear Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Jafar%20Biazar">Jafar Biazar</a>, <a href="https://publications.waset.org/search?q=Behzad%20Ghanbari"> Behzad Ghanbari</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, we are concerned with the further study for system of nonlinear equations. Since systems with inaccurate function values or problems with high computational cost arise frequently in science and engineering, recently such systems have attracted researcher-s interest. In this work we present a new method which is independent of function evolutions and has a quadratic convergence. This method can be viewed as a extension of some recent methods for solving mentioned systems of nonlinear equations. Numerical results of applying this method to some test problems show the efficiently and reliability of method.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=System%20of%20nonlinear%20equations." title="System of nonlinear equations.">System of nonlinear equations.</a> </p> <a href="https://publications.waset.org/13521/a-modification-on-newtons-method-for-solving-systems-of-nonlinear-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/13521/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/13521/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/13521/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/13521/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/13521/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/13521/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/13521/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/13521/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/13521/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/13521/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/13521.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">1593</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">1238</span> Numerical Treatment of Block Method for the Solution of Ordinary Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=A.%20M.%20Sagir">A. M. Sagir</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>Discrete linear multistep block method of uniform order for the solution of first order initial value problems (IVPs) in ordinary differential equations (ODEs) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. Furthermore, a stability analysis and efficiency of the block method are tested on ordinary differential equations, and the results obtained compared favorably with the exact solution.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Block%20Method" title="Block Method">Block Method</a>, <a href="https://publications.waset.org/search?q=First%20Order%20Ordinary%20Differential%20Equations" title=" First Order Ordinary Differential Equations"> First Order Ordinary Differential Equations</a>, <a href="https://publications.waset.org/search?q=Hybrid" title=" Hybrid"> Hybrid</a>, <a href="https://publications.waset.org/search?q=Self%20starting." title=" Self starting. "> Self starting. </a> </p> <a href="https://publications.waset.org/9997352/numerical-treatment-of-block-method-for-the-solution-of-ordinary-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/9997352/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/9997352/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/9997352/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/9997352/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/9997352/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/9997352/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/9997352/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/9997352/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/9997352/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/9997352/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/9997352.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">2794</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">1237</span> A Numerical Method for Diffusion and Cahn-Hilliard Equations on Evolving Spherical Surfaces</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Jyh-Yang%20Wu">Jyh-Yang Wu</a>, <a href="https://publications.waset.org/search?q=Sheng-Gwo%20Chen"> Sheng-Gwo Chen</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we present a simple effective numerical geometric method to estimate the divergence of a vector field over a curved surface. The conservation law is an important principle in physics and mathematics. However, many well-known numerical methods for solving diffusion equations do not obey conservation laws. Our presented method in this paper combines the divergence theorem with a generalized finite difference method and obeys the conservation law on discrete closed surfaces. We use the similar method to solve the Cahn-Hilliard equations on evolving spherical surfaces and observe stability results in our numerical simulations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Conservation%20laws" title="Conservation laws">Conservation laws</a>, <a href="https://publications.waset.org/search?q=diffusion%20equations" title=" diffusion equations"> diffusion equations</a>, <a href="https://publications.waset.org/search?q=Cahn-Hilliard%20Equations" title=" Cahn-Hilliard Equations"> Cahn-Hilliard Equations</a>, <a href="https://publications.waset.org/search?q=evolving%20surfaces." title=" evolving surfaces. "> evolving surfaces. </a> </p> <a href="https://publications.waset.org/10005661/a-numerical-method-for-diffusion-and-cahn-hilliard-equations-on-evolving-spherical-surfaces" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10005661/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10005661/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10005661/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10005661/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10005661/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10005661/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10005661/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10005661/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10005661/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10005661/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10005661.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">1504</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">1236</span> Spline Collocation for Solving System of Fredholm and Volterra Integral Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=N.%20Ebrahimi">N. Ebrahimi</a>, <a href="https://publications.waset.org/search?q=J.%20Rashidinia"> J. Rashidinia</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, numerical solution of system of Fredholm and Volterra integral equations by means of the Spline collocation method is considered. This approximation reduces the system of integral equations to an explicit system of algebraic equations. The solution is collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula. The error analysis of proposed numerical method is studied theoretically. The results are compared with the results obtained by other methods to illustrate the accuracy and the implementation of our method.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Convergence%20analysis" title="Convergence analysis">Convergence analysis</a>, <a href="https://publications.waset.org/search?q=Cubic%20B-spline" title=" Cubic B-spline"> Cubic B-spline</a>, <a href="https://publications.waset.org/search?q=Newton-%0D%0ACotes%20formula" title=" Newton- Cotes formula"> Newton- Cotes formula</a>, <a href="https://publications.waset.org/search?q=System%20of%20Fredholm%20and%20Volterra%20integral%20equations." title=" System of Fredholm and Volterra integral equations."> System of Fredholm and Volterra integral equations.</a> </p> <a href="https://publications.waset.org/9999855/spline-collocation-for-solving-system-of-fredholm-and-volterra-integral-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/9999855/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/9999855/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/9999855/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/9999855/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/9999855/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/9999855/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/9999855/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/9999855/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/9999855/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/9999855/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/9999855.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">2198</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">1235</span> Refitting Equations for Peak Ground Acceleration in Light of the PF-L Database</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=M.%20Bre%C5%A1ka">M. Breška</a>, <a href="https://publications.waset.org/search?q=I.%20Peru%C5%A1"> I. Peruš</a>, <a href="https://publications.waset.org/search?q=V.%20Stankovski"> V. Stankovski</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>The number of Ground Motion Prediction Equations (GMPEs) used for predicting peak ground acceleration (PGA) and the number of earthquake recordings that have been used for fitting these equations has increased in the past decades. The current PF-L database contains 3550 recordings. Since the GMPEs frequently model the peak ground acceleration the goal of the present study was to refit a selection of 44 of the existing equation models for PGA in light of the latest data. The algorithm Levenberg-Marquardt was used for fitting the coefficients of the equations and the results are evaluated both quantitatively by presenting the root mean squared error (RMSE) and qualitatively by drawing graphs of the five best fitted equations. The RMSE was found to be as low as 0.08 for the best equation models. The newly estimated coefficients vary from the values published in the original works.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Ground%20Motion%20Prediction%20Equations" title="Ground Motion Prediction Equations">Ground Motion Prediction Equations</a>, <a href="https://publications.waset.org/search?q=Levenberg-Marquardt%20algorithm" title=" Levenberg-Marquardt algorithm"> Levenberg-Marquardt algorithm</a>, <a href="https://publications.waset.org/search?q=refitting%20PF-L%20database." title=" refitting PF-L database."> refitting PF-L database.</a> </p> <a href="https://publications.waset.org/10000489/refitting-equations-for-peak-ground-acceleration-in-light-of-the-pf-l-database" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10000489/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10000489/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10000489/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10000489/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10000489/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10000489/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10000489/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10000489/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10000489/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10000489/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10000489.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">1495</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">1234</span> On Symmetries and Exact Solutions of Einstein Vacuum Equations for Axially Symmetric Gravitational Fields</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> Einstein vacuum equations, that is a system of nonlinear partial differential equations (PDEs) are derived from Weyl metric by using relation between Einstein tensor and metric tensor. The symmetries of Einstein vacuum equations for static axisymmetric gravitational fields are obtained using the Lie classical method. We have examined the optimal system of vector fields which is further used to reduce nonlinear PDE to nonlinear ordinary differential equation (ODE). Some exact solutions of Einstein vacuum equations in general relativity are also obtained. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Gravitational%20fields" title="Gravitational fields">Gravitational fields</a>, <a href="https://publications.waset.org/search?q=Lie%20Classical%20method" title=" Lie Classical method"> Lie Classical method</a>, <a href="https://publications.waset.org/search?q=Exact%20solutions." title=" Exact solutions."> Exact solutions.</a> </p> <a href="https://publications.waset.org/14108/on-symmetries-and-exact-solutions-of-einstein-vacuum-equations-for-axially-symmetric-gravitational-fields" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/14108/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/14108/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/14108/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/14108/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/14108/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/14108/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/14108/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/14108/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/14108/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/14108/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/14108.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">1934</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">1233</span> On the System of Nonlinear Rational Difference Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Qianhong%20Zhang">Qianhong Zhang</a>, <a href="https://publications.waset.org/search?q=Wenzhuan%20Zhang"> Wenzhuan Zhang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>This paper is concerned with the global asymptotic behavior of positive solution for a system of two nonlinear rational difference equations. Moreover, some numerical examples are given to illustrate results obtained.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Difference%20equations" title="Difference equations">Difference equations</a>, <a href="https://publications.waset.org/search?q=stability" title=" stability"> stability</a>, <a href="https://publications.waset.org/search?q=unstable" title=" unstable"> unstable</a>, <a href="https://publications.waset.org/search?q=global%0D%0Aasymptotic%20behavior." title=" global asymptotic behavior."> global asymptotic behavior.</a> </p> <a href="https://publications.waset.org/9998174/on-the-system-of-nonlinear-rational-difference-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/9998174/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/9998174/bibtex" target="_blank" rel="nofollow" class="btn btn-primary 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