In this paper, we present a numerical method for solving two-dimensional nonlinear Fredholm integral equations of the second kind on a non-rectangular domain. The method utilizes radial basis functions (RBFs) constructed on scattered points as a basis in the discrete collocation method. The proposed scheme is meshless, since it does not need any domain element and so it is independent of the geometry of domain. The method reduces the solution of the two-dimensional nonlinear integral equation to the solution of a nonlinear system of algebraic equations. Error analysis is presented for this method. Finally, numerical examples are included to show the validity and efficiency of the new technique.
