Solving PDEs Using the Natural Decomposition Transform Method

Abstract

In this article, a new method called the Natural Decomposition Transform Method (NDTM) is introduced. We use this method to obtain exact solutions for three different types of nonlinear partial differential equations (NLPDEs). The NDTM is based on the Natural transform method (NTM) and the Adomian decomposition method (ADM). The theoretical analysis of the NDTM is investigated for some equations and is calculated with easily computable terms. The results we obtained are compared with existing solutions obtained by other methods. One can conclude that the method is easy to use and efficient. Most of the symbolic and numerical computations were performed using Mathematica software.