A Study of Some Reliable Methods for Solving Fuzzy Volterra-Fredholm Integral Equations

Abstract

This paper mainly focuses on the recent advances in the approximated methods for solving fuzzy Volterra-Fredholm integral equations, namely, Adomian decomposition method, modified Adomian decomposition method, variational iteration method and homotopy analysis method. We converted fuzzy Volterra-Fredholm integral equation of the first kind to the second kind. That, a fuzzy Volterra-Fredholm integral equation has been converted to a system of Volterra-Fredholm integral equation in crisp case. The approximated methods using to find the approximate solution of this system and hence obtain an approximation for the fuzzy solution of the fuzzy Volterra-Fredholm integral equation. Moreover, we will prove the uniqueness of the solution and convergence of the proposed methods. The study outlines presumed features of these methods as well as sheds some light on advantages of one method over the other. To assess the accuracy of each method, algorithms with Mathematica 6 according is used. Also, some numerical examples are included to demonstrate the validity and applicability of the proposed techniques.