CONVERGENCE OF ADOMIAN'S METHOD APPLIED TO A CLASS OF VOLTERRA TYPE INTEGRO-DIFFERENTIAL EQUATIONS
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.
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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