Numerical solution of two-dimensional nonlinear Hammerstein fuzzy integral equations based on optimal fuzzy quadrature formula

In this paper, our aim is to provide an efficient iterative method of successive approximations to approximate solution of linear and nonlinear two-dimensional Hammerstein fuzzy integral equations by defining and developing an optimal quadrature formula for classes of two-dimensional fuzzy-number-valued functions of Lipschitz type. After the introduction of the optimal formula, we prove the convergence of the method of successive approximations used to approximate the solution of two-dimensional Hammerstein fuzzy integral equations and investigate the numerical stability of the presented method with respect to the choice of the first iteration. Finally, some illustrative numerical experiments confirm the theoretical results and demonstrate the accuracy of the method.