Superconvergence of the iterated Galerkin methods for Hammerstein equations

In this paper, the well known iterated Galerkin method and iterated Galerkin-Kantorovich regularization method for approximating the solution of Fredholm integral equations of the second kind are generalized to Hammerstein equations with smooth and weakly singular kernels. The order of convergence of the Galerkin method and those of superconvergence of the iterated methods are analyzed. Numerical examples are presented to illustrate the superconvergence of the iterated Galerkin approximation for Hammerstein equations with weakly singular kernels. Key words: the iterated Galerkin method, the iterated Galerkin-Kantorovich regularization, Hammerstein equations with weakly singular kernels, superconvergence. Mathematics Subject Classification (1990): 65B05, 45L10.