Abstract
In this paper a new method for solving Goursat problem is introduced using Reduced Differential Transform Method (RDTM). The approximate analytical solution of the problem is calculated in the form of series with easily computable components. The comparison of the methodology presented in this paper with some other well known techniques demonstrates the effectiveness and power of the newly proposed methodology.
Highlights
In this paper, we consider the standard form of the Goursat problem [1] [2] as provided below= uxt f ( x,t,u,ux,ut ), 0 ≤ x ≤ a, 0 ≤ t ≤ b (1)u ( x=,0) g ( x),u (= 0,t ) h(t ), g= (0) h= (0) u (0,0) (2)This equation has been examined by several numerical methods such as Runge-Kutta method, finite difference method, finite elements method and Adomian Decomposition Method (ADM).We will prove the applicability and effectiveness of Reduced Differential Transform Method (RDTM) on solving linear and non-linear Goursat problems
U ( x=,0) g ( x),u (= 0,t ) h(t ), g= (0) h= (0) u (0,0)
The linear homogeneous Goursat problem We first consider the linear homogeneous Goursat problem defined below uxt ( x,t ) = L (u ( x,t ))
Summary
We consider the standard form of the Goursat problem [1] [2] as provided below. This equation has been examined by several numerical methods such as Runge-Kutta method, finite difference method, finite elements method and Adomian Decomposition Method (ADM). We will prove the applicability and effectiveness of RDTM on solving linear and non-linear Goursat problems. The main advantage of RDTM is that it can be applied directly to the problems without requiring lineari-. How to cite this paper: Mohmoud, S. and Gubara, M. (2016) Reduced Differential Transform Method for Solving Linear and Nonlinear Goursat Problem.
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