Modification of Laplace Adomian Decomposition Method for Solving Nonlinear Volterra Integral and Integro-differential Equations based on Newton Raphson Formula

Dimple Rani, Vinod Mishra

Abstract

In this paper, we establish a modified Laplace decomposition method for nonlinear volterra integral and integro-differential equations. This technique differs from the general Laplace decomposition method because of the terms involved in Adomian polynomial.We have used Newton Raphson formula in place of the $u_{i}$ in Adomian polynomial. The proposed scheme is investigated with some illustrative examples and has given reliable results.

Keywords

Numerical Laplace Transform Method, Volterra Integral Equations(VIEs), Volterra Integro-differential Equations(VIDEs), Adomian Decomposition Method(ADM), Newton Raphson formula.

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