New approach to solve two-dimensional Fredholm integral equations

Abstract

In this paper, we present an efficient iterative method based on quadrature formula to solve two-dimensional nonlinear Fredholm integral equations. We investigate the convergence analysis of the proposed method. The error estimation is given in terms of uniform and partial modulus of continuity. In addition, we show the numerical stability analysis of the method with respect to the choice of the first iteration. Finally, some numerical experiments confirm the theoretical results and illustrate the accuracy of the method.