A new generalization of the differential transform method for solving boundary value problems

Abstract

In this article, we propose a new generalization of the differential transformation method (DTM), i.e., α-Parameterized Differential Transform Method (α-PDTM), for finding approximate solutions to the boundary value problems. We then apply the proposed method to two boundary value problems for different values of the parameter α. Afterwards, we compare its solutions with DTM and exact solutions. Moreover, we present several visual illustrations.