A new algorithm for calculating one-dimensional differential transform of nonlinear functions

A new technique for calculating the one-dimensional differential transform of nonlinear functions is developed in this paper. This new technique avoids the difficulties and massive computational work that usually arise from the standard method. The algorithm will be illustrated by studying suitable forms of nonlinearity. Several nonlinear ordinary differential equations, including Troesch’s and Bratu-type problems, are then solved to demonstrate the reliability and efficiency of the proposed scheme. The present algorithm offers a computationally easier approach to compute the transformed function for all forms of nonlinearity. This gives the technique much wider applicability.