In this paper, first, we introduce a successive approximation method in terms of a combination of Bernstein polynomials and block-pulse functions. The proposed method is given for solving two dimensional nonlinear fuzzy Fredholm integral equations of the second kind. Then, we present the convergence of the proposed method. Also we investigate the numerical stability of the method with respect to the choice of the first iteration. Finally, two numerical examples are presented to show the accuracy of the method.

In this paper, first, we apply the successive approximations method in terms of midpoint quadrature formula to solve nonlinear fuzzy Fredholm integral equations of the second kind (NFFIE-2). Considering some assumptions, we acquire a new error estimation. Moreover, we prove the convergence of the proposed method. Then, we study the numerical stability of the proposed method with respect to the first iteration choice. Eventually, to demonstrate the accuracy of the suggested method, we present two numerical examples.