Convergence of Adomian's Method Applied to a Class of Volterra Type Integro-Differential Equations

Convergence of Adomian decomposition method (ADM) is of a great importance when applied to different types of nonlinear equations. In this paper, the proof of convergence of ADM when applied to a class of nonlinear Volterra type integro-differential equations including the sufficient conditions guaranteeing existence and uniqueness is introduced. The k-th order integro-differential equation was transformed to corresponding equivalent system of $(k+1)$ Volterra integral equations. The equation and the equivalent system are solved. A comparison between the two solutions shows that this transformation simplifies the calculations.