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

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 uᵢ in Adomian polynomial. The proposed scheme is investigated with some illustrative examples and has given reliable results.