Generalizing of Differential Transform Method for Solving Nonlinear Differential Equations

[摘要] In this paper, the differential transform method (DTM) is proved to be an excellent tool to investigate analytical and numerical solutions of nonlinear ordinary differential equations. The concept of differential transformation is briefly presented and some well-known properties of this DTM are rewritten in a more generalized forms. Several classes of nonlinear differential equations are solved analytically and numerically, in order to show the efficiency of the DTM, and the fundamental algorithms are presented in Matlab language.

[关键词] Differential transform method;Nonlinear ordinary differential equation;Exact solution;Numerical investigation