Application of Variational Iteration Method for nth-Order Integro-Differential Equations

The variational iteration method [1, 2], which is a modified general Lagrange multiplier method, has been shown to solve effectively, easily, and accurately a large class of nonlinear problems with approximations which converges (locally) to accurate solutions (if certain Lipschitz-continuity conditions are met). It was successfully applied to autonomous ordinary differential equations and nonlinear partial differential equations with variable coefficients [3], to Schrödinger-KdV, generalized KdV and shallow water equations [4], to Burgers’ and coupled Burgers’ equations [5], to the linear Helmholtz partial differential equation [6], and recently to nonlinear fractional differential equations with Caputo differential derivative [7], and other fields [8 – 10]. Also, the variational iteration method is applied to fourth-order Volterra’s integro-differential equations [11] and J. H. He used it for solving some integro-differential equations [12] by choosing the initial approximate solution in the form of a exact solution with unknown constants. On the other hand, Golbabai and Javidi solved the nth-order integrodifferential equations [13] by transforming to a system of ordinary differential equations and using the homotopy method. The purpose of this paper is to extend the analysis of the variational iteration method for solving the general nth-order integro-differential equations as follows: