The Adomian decomposition method for numerical solution of first-order differential equations

Abstract

In this paper, the Adomian decomposition method (ADM) is a powerful method which considers the approximate solution of a non-linear equation as an infinite series which usually converges to the exact solution. In this paper, this method is proposed to solve some first-order differential equations. It is shown that the series solutions converge to the exact solution for each problem. It is observed that the method is particularly suited for initial value problems with oscillatory and exponential solutions.