Convergence analysis of Galerkin and multi-Galerkin methods for nonlinear-Hammerstein integral equations on the half-line using Laguerre polynomials

Abstract

In this paper, we consider Galerkin and multi-Galerkin methods and their iterated versions for solving the nonlinear Hammerstein-type integral equation on the half-line with sufficiently smooth kernels, using Laguerre polynomials as basis functions. We obtain optimal convergence results in iterated-Galerkin method in both infinity and weighted -norms. We also obtain the superconvergence results in both multi-Galerkin and iterated multi-Galerkin methods, respectively, in weighted -norm. Numerical results are presented to validate the theoretical results.