The Combined RKM and ADM for Solving Nonlinear Weakly Singular Volterra Integrodifferential Equations

Abstract

The reproducing kernel method (RKM) and the Adomian decomposition method (ADM) are applied to solve $n$th-order nonlinear weakly singular Volterra integrodifferential equations. The numerical solutions of this class of equations have been a difficult topic to analyze. The aim of this paper is to use Taylor’s approximation and then transform the given $n$th-order nonlinear Volterra integrodifferential equation into an ordinary nonlinear differential equation. Using the RKM and ADM to solve ordinary nonlinear differential equation is an accurate and efficient method. Some examples indicate that this method is an efficient method to solve $n$th-order nonlinear Volterra integro-differential equations.