In this paper, we present a reliable algorithm for solving a system of Volterra integro-differential equations (VIDE) using He's Homotopy Perturbation Method (HHPM) [9,10] and spectral methods [12]. This method converts a system of Volterra integro-differential equations to the system of linear algebraic equations. Some illustrative examples have been presented to illustrate the implementation of the algorithm and efficiency of the method.

In this paper, He's Homotopy Perturbation Method (HHPM), by construction, produces approximate solutions of nonlinear integro-differential equations [2]. The purpose of this paper is to extend the He's Homotopy Perturbation method to the nonlinear integro-differential equations. Efficient error estimation for the He's Homotopy Perturbation method is also introduced. Details of this method are presented and compared with Single-Term Haar Wavelet Series (STHWS) method [2] numerical results along with estimated errors are given to clarify the method and its error estimator.