Numerical Solutions of the Linear Volterra Integro-differential Equations : Homotopy Perturbation Method and Finite Difference Method

In the research, special type of linear volterra integro-differential equations is considered. This paper compares the Homotopy perturbation method (HPM) with finite difference method for solving these equations. HPM is an analytical procedure for finding the solutions of problems which is based on the constructing a Homotopy with an imbedding parameter p that is considered as a small parameter. The finite difference method, based upon Simpson rule and Trapezoidal rule, transforms the volterra integro-differential equation into a matrix equation. The results of applying these methods to the linear integro-differential equation show the simplicity and efficiency of these methods.