Differential Transform Method for Differential Equations

Abstract

The differential transform method was firstly introduced by Zhou before thirty years ago. This method is a semi-analytical numerical method for solving differential equations. Indeed, the differential transform method is based on Taylor series expansion, in a different manner, in which the differential equation is converted into a recurrence relation to get a series solution in terms of polynomials. This thesis is mainly concerned with the differential transform method for both ordinary and partial differential equations. Firstly, we use the one dimensional differential transform method to solve initial value problems as well as boundary value problems for ordinary differential equations. In addition, we present recent modifications of differential transform method that improve its algorithm. Secondly, we solve initial and boundary value problems for partial differential equations by using two dimensional differential transform method, reduced differential transform method and Laplace differential transform method.