Laplace Decomposition Method for the System of Linear and Non-Linear Ordinary Differential Equations

Abstract

In this paper we use Modified form of Adomian’s Decomposition Method Laplace, which is a mixture of Laplace transforms and Adomian’s Decomposition Method called the Laplace Decomposition Method (LDM) to solve the system of ordinary differential equation of the first order and an ordinary differential equation of any order by converting it into a system of differential equation of order one. Some examples are presented to show the ability of the method for linear and non-linear systems of differential equations also present the comparison of their solution with the exact solution through graphically.

Keywords: Laplace Transformation, Adomian’s Decomposition Method (ADM), System of differential equation, linear differential equation and non-linear ordinary differential equation.