Solution of System of Defferential Equations by Defferential Trans From Method

Abstract

A new technique for calculating the one–dimensional differential transform of nonlinear functions. This new technique the difficulties and massive computational work that usually a rise from the standard method . The algorithm will be illustrated by studying suitable forms of nonlinearity. Two- dimensional differential transform method of solution of the initial value problem for partial differential equation ( PDEs ) have been studied. New theorems have been added and some linear and nonlinear PDEs solved by using this method. The method can be easily applied to linear or nonlinear problems and is capable of reducing the size of computational work. Three –dimensional differential transform method has been introduced and fundamental theorems have been defined for the first time. Moreover, as an application of two and three-dimensional differential transform, exact solutions of linear and non-linear systems of partial differential equations have been investigated. The results of the present method are compared very well with those obtained by analytical method. With this method exact solution may be obtained without any need of cumbersome work and if is an useful tool for analytical and numerical solutions. Differential transform method can easily be applied to differential – algebraic equations ( DAEs ) and series solutions are obtained. The differential transformation which is applied to solve eigenvalue problems and to solve partial differential equations ( PDEs ) is proposed in this study. ‫‪First, using the one – dimensional differential transformation to construct the‬‬ ‫‪eigenvalues and the normalized eigenfunctions for the differential equation of the‬‬ ‫. ‪second- and the fourth- order‬‬ ‫)‪Second, using the two- dimensional differential transformation to solve (PDEs‬‬ ‫‪of the first- and second- order with constant coefficients. In both cases, a set of‬‬ ‫‪difference equations is derived and the calculated results are compared closely with‬‬ ‫.‪the results obtained by other analytical methods‬‬