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695 articles for “Equation”
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Research ArticleOpen accessEvery word in the titleGlobal Behavior of a Higher Order Difference EquationAlaa E. Hamza, R. Khalaf-AllahIn this work we study the asymptotic stability of the nonnegative equilibrium points of the difference equation. We discuss the conditions under which there exist prime period two solutions and semicycles. Finally we investigate the oscillation and the existence of unbounded solutions. …Journal of Mathematics and Statistics, Vol. 3, Issue 1 · 31 Mar 2007 · 7,059 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleOn Self-similar Solution of Non-linear Diffusion Equation with Convection TermB. I. Olajuwon, A. O. PopoolaWe consider the self-similar solution of non-linear diffusion equation with convection term. We examine the existence and uniqueness of solution of the problem. The numerical result is presented as concentration profile for various values of m, the diffusion index. …Journal of Mathematics and Statistics, Vol. 2, Issue 4 · 31 Dec 2006 · 6,315 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleThe Solution of Heat Conduction Equation with Mixed Boundary ConditionsNaser AbdelrazaqThe study is devoted to determine a solution for a non-stationary heat equation in axial symmetric cylindrical coordinates under mixed discontinuous boundary of the first and second kind conditions, with the aid of a Laplace transform and separation of variables method used to solve the considered problem which is the dual integral equations method. …Journal of Mathematics and Statistics, Vol. 2, Issue 1 · 31 Mar 2006 · 7,817 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleEffects of Higher Order Dispersion Terms in the Nonlinear Schrodinger EquationRobert Beech, Frederick OsmanThis study presents a concise graphical analysis of solitonic solutions to a nonlinear Schrodinger equation (NLSE). A sequence of code using the standard NDSolve function has been developed in Mathematica to investigate the acceptable accuracy of the NLSE in relatively small ranges of the dispersive parameter space. An operator splitting approach was used in the numerical solutions to expand the … …American Journal of Applied Sciences, Vol. 2, Issue 9 · 30 Sep 2005 · 6,493 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleProgramming of the Generalized Nonlinear Paraxial Equation for the Formation of Solitons with MathematicaFrederick Osman, Robert BeechThis study presents the nonlinearity and dispersion effects involved in the propagation of optical solitons which can be understood by using a numerical routine to solve the Generalized Nonlinear Paraxial equation. A sequence of code has been developed in Mathematica, to explore in depth several features of the optical soliton’s formation and propagation. These numerical routines were implemented through the … …American Journal of Applied Sciences, Vol. 1, Issue 2 · 30 Jun 2004 · 6,787 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleParallel Iterative Algorithms with Accelerate Convergence for Solving Implicit Difference EquationsQing-Fu Liu, Wei-Jun Zhong, Mancho ManevThis study focuses on the solution of implicit difference equations, which are very difficult to compute in parallel for the diffusion equation. For improving the convergence rates and the properties of gradual-approach convergence of Segment-Classic-Implicit-Iterative (SCII) and Segment-Crank-Nicolson-Iterative (SCNI) algorithms realizing efficient iterative computation in parallel by segmenting grid domains, SCII and SCNI algorithms with accelerated convergence are studied and … …American Journal of Applied Sciences, Vol. 1, Issue 1 · 31 Mar 2004 · 6,801 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleOn the General Solution to the Bratu and Generalized Bratu EquationsLucas Hervé Koudahoun, Jean Akande, Damien Kêgnidé Kolawolé Adjaï et al.This work shows that the Bratu equation belongs to a general class of Liénard-type equations for which the general solution may be exactly and explicitly computed within the framework of the generalized Sundman transformation. In this perspective the exact solution of the Bratu nonlinear two-point boundary value problem as well as of some well-known Bratu-type problems have been determined. …Journal of Mathematics and Statistics, Vol. 14, Issue 1 · 14 Jul 2018 · 7,689 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleq- sl2 and Associated Wave and Heat EquationsSami H. AltoumFor q∈(0, 1), the q- deformation of the sl2 Lie algebra (denoted by q-sl2) is introduced and we give its representation. The heat and wave equations associated to the genrators of the q-sl2 are studied. …American Journal of Applied Sciences, Vol. 15, Issue 5 · 12 May 2018 · 7,807 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleDynamics and Stability of q-Fractional Order Pantograph Equations With Nonlocal ConditionVivek Devaraj, Kuppusamy Kanagarajan, Seenith SivasundaramThis paper deals with some existence and Ulam-Hyers-q-Mittag-Leffler stability results for q-fractional order pantograph equation. An application is made of a Darbo's fixed point theorem for the existence of solutions. …Journal of Mathematics and Statistics, Vol. 14, Issue 1 · 10 Feb 2018 · 7,430 accessesView PDFCite
Research NotesOpen accessEvery word in the titleA Note on a New Method of Investigation of Solutions of Boundary Value Problems for the Elliptic Type Equations of the First OrderNihan A. Aliyev, Alexander A. Katz, Metanet B. MursalovaThe paper deals with investigation of the solutions of the boundary value problem for the Cauchy-Riemann equation on the curvelinear strip in the real plane. Here the boundary conditions are in the special type and are fundamental with respect to the direction solutions are used. An analytic form of the solution of considered boundary value problem is obtained. …Journal of Mathematics and Statistics, Vol. 14, Issue 1 · 17 Jan 2018 · 7,211 accessesView PDFCite