Numerical solution of nonlinear Volterra-Fredholm integro-differential equations using Homotopy Analysis Method

The use of homotopy analysis method to approximate the solution of nonlinear Volterra-Fredholm integro-differential equation is proposed in this paper. In this case, the existence and uniqueness of the obtained solution and convergence of the method are proved. The accuracy of the proposed numerical scheme is examined by comparing with the modified Adomian decomposition method and Taylor polynomial method in the example. Also, the cost of operations in the algorithms are obtained to demonstrate the efficiency of the presented method. © 2010 Korean Society for Computational and Applied Mathematics.