The Adomian Decomposition Method and the Differential Transform Method for Numerical Solution of Multi-Pantograph Delay Differential Equations

Abstract

In this paper, the Adomian Decomposition Method (ADM) and the Differential Transform Method (DTM) are applied to solve the multi-pantograph delay equations. The sufficient conditions are given to assure the convergence of these methods. Several examples are presented to demonstrate the efficiency and reliability of the ADM and the DTM; numerical results are discussed, compared with exact solution. The results of the ADM and the DTM show its better performance than others. These methods give the desired accurate results only in a few terms and in a series form of the solution. The approach is simple and effective. These methods are used to solve many linear and nonlinear problems and reduce the size of computational work.