On Finding Exact Solutions to Coupled Systems of Partial Differential Equations by the NDM

Mahmoud Saleh Rawashdeh, Shehu Maitama

Abstract

In this article, we develop a new method called the Natural Decomposition Method (NDM). We use the NDM to find exact solutions for coupled systems of linear and nonlinear partial differential equations. The proposed method is a combination of the Natural Transform Method (NTM) and Adomian Decomposition method (ADM). Besides, the NDM avoid round-off errors which leads to solutions in closed form. The new method always lead to an exact or approximate solution in the form of rapidly convergence series. Hence, the Natural Decomposition Method is elegant refinement of the existing methods and can easily be used to solve a wide class of Linear and Nonlinear Partial Differential Equations.