Gauss-Legendre type quadrature iterative method for fuzzy Fredholm integral equations

In this paper we obtain an iterative method for the numerical solution of second kind fuzzy Fredholm integral equations by applying appropriate composite fuzzy quadrature formula. We approach a general fuzzy quadrature formula and show that the three-point and four-point Gauss-Legendre type fuzzy quadrature formulas are the best choice from computational cost and accuracy point of view. The convergence of the method is proved by providing the error estimates expressed in terms of the Lipschitz constant of the Picard iterations. Some numerical results confirm the obtained theoretical result and illustrate the performances of the three point Gauss-Legendre method in comparison with the techniques generated by the fuzzy Newton-Cotes and Gauss-Lobatto quadrature formulas, the results being tested on the Simpson and on the four point Gauss-Legendre and Gauss-Lobatto quadrature formulas in particular. The numerical experiment suggests that five point or more point fuzzy quadrature formulas are useless due to the accumulation of errors and the grown computational cost.