Superconvergence Results for Weakly Singular Fredholm–Hammerstein Integral Equations

Abstract

In this article, we consider the multi-Galerkin method for solving the Fredholm–Hammerstein integral equations with weakly singular kernels, using piecewise polynomial bases. We show that multi-Galerkin method has order of convergence for the algebraic kernel, whereas for logarithmic kernel, it converges with the order in uniform norm, where h is the norm of the partition and r is the smoothness of the solution. We also discuss the iterated multi-Galerkin method. We prove that iterated multi-Galerkin method has order of convergence for the algebraic kernel and for logarithmic kernel, it has order of convergence of order in uniform norm. Numerical examples are given to illustrate the theoretical results.