Superconvergent spectral projection and multi-projection methods for nonlinear Fredholm integral equations

Abstract

In this article, we apply Galerkin and multi-Galerkin methods based on Kumar Sloan technique using Legendre polynomial basis functions for approximating the nonlinear Fredholm Hammerstein integral equations with the smooth kernels as well as the weakly singular algebraic and logarithmic kernels. We show that we are getting the improved superconvergence rates for Galerkin and multi-Galerkin methods based on Kumar Sloan technique without the need for the iterated Galerkin and the iterated multi-Galerkin methods. Infact without going to the iterated versions, we obtain the superconvergence rates equal to the convergence rates of iterated Galerkin and iterated multi-Galerkin methods. Theoretical results have been illustrated with numerical experiments.