Fuzzy trapezoidal cubature rule and application to two-dimensional fuzzy Fredholm integral equations

Abstract

In this paper, we construct the fuzzy trapezoidal cubature rule providing its remainder estimate for the case of Lipschitzian functions. As an application, we propose an iterative numerical method in order to approximate the solution of nonlinear fuzzy Fredholm integral equations in two variables, the fuzzy cubature rule being used in the construction of the numerical method. The convergence of the method is proved and tested through a numerical experiment, that confirms the obtained theoretical results.