Modified Variational Homotopy Perturbation Method for Nonlinear Volterra Integro-differential Equations

In this paper, we apply the Modified Variational Homotopy Method (MVHPM) for the numerical solution of nonlinear Volterra integro-differential equations. The method is an elegant mixture of Variational Iteration and Homotopy Perturbation Methods. The modification is effected at the approximation stage. This modification is the addition of the coecients of the least and highest powers of the homotopy parameter, p, instead of the addition of all the coefficients. The method is applied directly without discretization, linearization or perturbation. Two numericalExamples are considered to demonstrate the effectiveness and performance accuracy of the method. The resulting numerical evidences show the method is highly reliable, effective and accurate as compared to existing methods the Variational Homotopy Method (VHPM) and the Variational Iteration Method (VIM), available in the literature.