Communications in Numerical Analysis
Volume 2012 (2012), Article ID cna-00108, 20 Pages
The Use of Iterative Methods to Solve Two-Dimensional Nonlinear Volterra-Fredholm Integro-Differential Equations
Sh. Sadigh Behzadi *
Department of Mathematics, Islamic Azad University, Central Tehran Branch, Tehran, Iran.
* Corresponding author. Email address: firstname.lastname@example.org; Tel: +989123409593
Received: 18 October 2011; Accepted: 16 Februar 2012
Copyright © 2012 Sh. Sadigh Behzadi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.
Keywords: Two-dimensional Volterra and Fredholm integral equations; Integro-differential equations; Modified Adomian decomposition method; Variational iteration method; Homotopy analysis method; Modified homotopy perturbation method.
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