Solutions of classes of differential equations using modified differential transform method

Abstract

This paper proposed a numerical approximation scheme for solving singular two-point boundary value problems. This approach is based on a truncated series obtained by differential transform (DT) method, the Laplace transformation (LT) approach and process of Pade approximants. The modified differential transform method ´ (MDTM) aims to overcome the difficulty of solving these types of problems and gives a good approximation for the true solution in a large region. Some illustrative examples are presented to demonstrate the effectiveness and applicability of the new method and the obtained results are compared with the exact solution.