Applications of Adaptive Multi Step Differential Transform Method to Singular Perturbation Problems Arising in Science and Engineering

Abstract

In this paper, piecewise-analytical and numerical solutio ns of singular perturbation initial-value problems are obt ained by an adaptive multi-step differential transform method (MsDTM). The principle of the method is introduced, and then applied to different types of practical problems arising in science an d engineering. Analytical and numerical solutions are obtained using piecewise convergent series with easily computable components over a sequence of variable-length sub-intervals. Numerical results are compared to those obtained by the classical MsDTM and the Runge-Kutta method. The results demonstrate the reliability and efficie ncy of the method in solving the considered problems.