The Use of Iterative Methods to Solve Two-Dimensional Nonlinear Volterra-Fredholm Integro-Differential Equations

Abstract

In this present paper, we solve a two-dimensional nonlinear Volterra-Fredholm integro-differential equation by using the following powerful, efficient but simple methods: (i) Modified Adomian decomposition method (MADM), (ii) Variational iteration method (VIM), (iii) Homotopy analysis method (HAM) and (iv) Modified homotopy perturbation method (MHPM). The uniqueness of the solution and the convergence of the proposed methods are proved in detail. Numerical examples are studied to demonstrate the accuracy of the presented methods.