Application of the Adomian Decomposition Method to Solve Ordinary Differential Equations

Abstract

The Adomian Decomposition Method (ADM) is a semi-analytical technique for solving linear and nonlinear ordinary differential equations without linearization, discretization, or perturbation. This paper presents the systematic application of ADM to different classes of differential equations, ranging from simple nonlinear equations to higher-order linear cases. Five illustrative examples are worked out in detail to demonstrate the power, flexibility, and efficiency of the method. The results show that ADM provides rapidly converging series solutions that agree closely with exact or known solutions, establishing it as a useful alternative to traditional analytical and numerical methods