Two-Grid Iterative Method for a Class of Fredholm Functional Integral Equations based on the Radial Basis Function Interpolation

Abstract

In this paper, we discuss a two-grid iterative method for solving a class of Fredholmfunctional integral equations based on the radial basis function interpolation. Firstly,the existence and uniqueness of the solution are proved by Banach fixed point theorem.Secondly, the algorithm and convergence analysis of the radial basis function approximationmethod is given on the coarse grid. Thirdly, the fine grid iterative solution and convergenceresults are obtained. Finally, the validity and reliability of the theoretical analysis areverified by two numerical experiments.