By using the properties of strong fuzzy Henstock integrals, the existence theorems of solution for a kind of the discontinuous fuzzy Fredholm integral equations are established. The results are generalizations of earlier investigation for fuzzy continuous systems.

In this paper an expansion method, based on Legendre or any orthogonal polynomials, is developed to find numerical solutions of two-dimensional linear Fredholm integral equations. We estimate the error of the method, and present some numerical examples to demonstrate the accuracy of the method. 2000 Mathematics subject classification: 65R20.

The purpose of this paper is two-fold. First, we develop the Petrov-Galerkin method and the iterated Petrov-Galerkin method for a class of nonlinear Hammerstein equations. Alpert [1] established a class of wavelet basis and applied it to approximate solutions of the Fredholm second kind integral equations by the Galerkin method. He then demonstrated an advantage of a wavelet basis application t...

‎In this paper‎, ‎firstly‎, ‎we review approximation of fuzzy functions‎ ‎by fuzzy bicubic splines interpolation and present a new approach‎ ‎based on the two-dimensional fuzzy splines interpolation and‎ ‎iterative method to approximate the solution of two-dimensional‎ ‎linear fuzzy Fredholm integral equation (2DLFFIE)‎. ‎Also‎, ‎we prove‎ ‎convergence analysis and numerical stability analysis ...

In this paper, the two-dimensional triangular orthogonal functions (2D-TFs) are applied for solving a class of nonlinear two-dimensional Volterra integral equations. 2D-TFs method transforms these integral equations into a system of linear algebraic equations. The high accuracy of this method is verified through a numerical example and comparison of the results with the other numerical methods.

‎‎‎In this paper‎, ‎we develop multi-step methods to solve a class of two-dimensional nonlinear Volterra integral equations (2D-NVIEs) of the first kind‎. ‎Here‎, ‎we convert a 2D-NVIE of the first kind to a one-dimensional linear VIE of the first kind and then we solve the resulted equation numerically by multi-step methods‎. ‎We also verify convergence and error analysis of the method‎. ‎At t...