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
