On the Effective Region of Convergence of the Decomposition Series Solution

Abstract

In this paper we investigate the domain of convergence of the Adomian series solution based on the computational results for several examples. We demonstrate how the domain of convergence can be extended by introducing a parameter c in the definition of the zeroth-order and first-order solution components u0 and u1. Furthermore we generalize the concept of the convergence parameter c from a two-term partition of the initial condition to a multiple-term partition with the design of expanding the domain of convergence of the Adomian series solutions for nonlinear differential equations.