Abstract
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.
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