Modification of Laplace Adomian Decomposition Method for Solving Nonlinear Volterra Integral and Integro-differential Equations based on Newton Raphson Formula (European Journal of Pure and Applied Mathematics, 2018)
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.