Using The Differential Transformation Method (DTM) to Solving Ordinary Differential Equations

Abstract

The differential transformation method (DTM) was first introduced by Zhou 37 years ago. This method is a semi-analytical numerical method for solving homogeneous or inhomogeneous linear ordinary differential equations. Indeed, the differential transform method is based on Taylor series expansion in a different way, in which the differential equation is turned into a recurrence relation to provide a series solution in terms of polynomials. This research is concerned with the differential transformation method for both ordinary and partial differential equations. To solve initial value and boundary value problems for ordinary differential equations, we use the one-dimensional differential transform technique. Furthermore, we present new modifications to the differential transformation method that improve its algorithm. The differential transformation method is capable to reduce the size of calculations and handles homogeneous or inhomogeneous linear ordinary differential equations directly. Seven examples are considered for the numerical illustrations of this method. The results demonstrate the reliability and efficiency of this method for such problems.