University of TabrizComputational Methods for Differential Equations2345-39821120131201A High Order Approximation of the Two Dimensional Acoustic Wave Equation with Discontinuous Coefficients115231ENJavad FarziSahand University Of TechnologyJournal Article20131212This paper concerns with the modeling and construction of a fifth order method for two dimensional acoustic wave equation in heterogenous media. The method is based on a standard discretization of the problem on smooth regions and a nonstandard method for nonsmooth regions. The construction of the nonstandard method is based on the special treatment of the interface using suitable jump conditions. We derive the required linear systems for evaluation of the coefficients of such a nonstandard method. The given novel modeling provides an overall fifth order numerical model for two dimensional acoustic wave equation with discontinuous coefficients.University of TabrizComputational Methods for Differential Equations2345-39821120131220Chebyshev Spectral Collocation Method for Computing Numerical Solution of Telegraph Equation1629242ENM. JavidiUniversity of TabrizJournal Article20131212In this paper, the Chebyshev spectral collocation method(CSCM) for one-dimensional linear hyperbolic telegraph equation is presented. Chebyshev spectral collocation method have become very useful in providing highly accurate solutions to partial differential equations. A straightforward implementation of these methods involves the use of spectral differentiation matrices. Firstly, we transform telegraph equation to system of partial differential equations with initial condition. Using Chebyshev differentiation matrices yields a system of ordinary differential equations. Secondly, we apply fourth order Runge-Kutta formula for the numerical integration of the system of ODEs. Numerical results verified the high accuracy of the new method, and its competitive ability compared with other newly appeared methods.University of TabrizComputational Methods for Differential Equations2345-398211201312202-stage explicit total variation diminishing preserving Runge-Kutta methods3038259ENM. Mehdizadeh KhalsaraeiUniversity of MaraghehF. KhodadostiUniversity of Maragheh0000-0003-4315-3907Journal Article20131214In this paper, we investigate the total variation diminishing property for a class of 2-stage explicit Rung-Kutta methods of order two (RK2) when applied to the numerical solution of special nonlinear initial value problems (IVPs) for (ODEs). Schemes preserving the essential physical property of diminishing total variation are of great importance in practice. Such schemes are free of spurious oscillations around discontinuities.University of TabrizComputational Methods for Differential Equations2345-39821120131220Existence and multiplicity of positive solutions for a coupled system of perturbed nonlinear fractional differential equations3954260ENKazem GhanbariSahand University of
TechnologyYousef GholamiSahand University of
TechnologyJournal Article20131214In this paper, we consider a coupled system of nonlinear fractional differential equations (FDEs), such that both equations have a particular perturbed terms. Using emph{Leray-Schauder} fixed point theorem, we investigate the existence and multiplicity of positive solutions for this system.University of TabrizComputational Methods for Differential Equations2345-39821120131220Parameter determination in a parabolic inverse problem in general dimensions5570277ENReza ZolfaghariSalman Farsi University of KazerunJournal Article20131216It is well known that the parabolic partial differential equations in two or more space dimensions with overspecified boundary data, feature in the mathematical modeling of many phenomena. In this article, an inverse problem of determining an unknown time-dependent source term of a parabolic equation in general dimensions is considered. Employing some transformations, we change the inverse problem to a Volterra integral equation of convolution-type. By using an explicit procedure based on Sinc function properties, the resulting integral equation is replaced by a system of linear algebraic equations. The convergence analysis is included, and it is shown that the error in the approximate solution is bounded in the infinity norm by the condition number and the norm of the inverse of the coefficient matrix multiplied by a factor that decays exponentially with the size of the system. Some numerical examples are given to demonstrate the computational efficiency of the method.University of TabrizComputational Methods for Differential Equations2345-39821120131220The modified simplest equation method and its application7177306ENM. AkbariUniversity of GuilanJournal Article20131217In this paper, the modified simplest equation method is successfully implemented to find travelling wave solutions of the generalized forms $B(n,1)$ and $B(-n,1)$ of Burgers equation. This method is direct, effective and easy to calculate, and it is a powerful mathematical tool for obtaining exact travelling wave solutions of the generalized forms $B(n,1)$ and $B(-n,1)$ of Burgers equation and can be used to solve other nonlinear partial differential equations in mathematical physics.