Application of the Variational Iteration Method to Nonlinear Volterra’s Integro-Differential Equations

He’s variational iteration method [1, 2], which is a modified general Lagrange multiplier method [3], has been shown to solve effectively, easily and accurately a large class of nonlinear problems with approximations which converge quickly to accurate solutions. It was successfully applied to autonomous ordinary differential equations [4], nonlinear partial differential equations with variable coefficients [5], SchrödingerKorteweg-de Vries (KDV), generalized KDV and shallow water equations [6], Burgers’ and coupled Burgers’ equations [7], the linear Helmholtz partial differential equation [8] and recently to nonlinear fractional differential equations with Caputo differential derivative [9], and other fields [10 – 12]. Also, J. H. He used the variational iteration method for solving some integro-differential equations [13] by choosing the initial approximate solution in the form of an exact solution with unknown constants. The aim of this paper is to extend the analysis of the variational iteration method to solve the general nonlinear Volterra’s integro-differential equations of type