Natural decomposition approximation solution for second order nonlinear differential equations

Abstract

In this article, I introduce the Natural Decomposition Method (NDM) to solve nonlinear second order differential equations. I use the NDM to obtain exact solutions for three different types of nonlinear second order ordinary differential equations. The NDM is the combination of Natural transform method (NTM) and the Adomian decomposition method (ADM). The proposed method gives exact solutions in the form of a rapid convergence series and applied directly without using any linearization, discretization, transformation, or taking some restrictive assumptions. Therefore, the Natural Decomposition Method is an outstanding mathematical tool for solving nonlinear second order ordinary differential equation. One can conclude that the NDM is efficient and easy to use.