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

Abstract

<div>This paper mainly focuses on the recent advances in the some approximated methods for solving fuzzy Volterra-Fredholm integral equations, namely, Adomian decomposition method, variational iteration method and homotopy analysis method. We converted fuzzy Volterra-Fredholm integral equation to a system of Volterra-Fredholm integral equation in crisp case. The approximated methods using to find the approximate solutions of this system and hence obtain an approximation for the fuzzy solution of the fuzzy Volterra-Fredholm integral equation. 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</div><div>of the proposed techniques.</div>This paper mainly focuses on the recent advances in the some approximated methods for solvingfuzzy Volterra-Fredholm integral equations, namely, Adomian decomposition method, variational iterationmethod and homotopy analysis method. We converted fuzzy Volterra-Fredholm integral equation to asystem of Volterra-Fredholm integral equation in crisp case. The approximated methods using to find theapproximate solutions of this system and hence obtain an approximation for the fuzzy solution of the fuzzyVolterra-Fredholm integral equation. To assess the accuracy of each method, algorithms with Mathematica 6according is used. Also, some numerical examples are included to demonstrate the validity and applicabilityof the proposed techniques.