Adaptive multi-step differential transformation method to solving nonlinear differential equations

In this paper, we propose a fast and effective adaptive algorithm for the multi-step differential transformation method (MsDTM). This approach named as the adaptive MsDTM is applied to a number of nonlinear differential equations and numerical results are given. At the same time, a comparison between the MsDTM and the adaptive MsDTM reveals that the proposed approach is an efficiency tool for solving the considered equations using fewer time steps.