Convergence analysis of Galerkin and multi-Galerkin methods on unbounded interval using Hermite polynomials

Abstract

We consider in this paper the Galerkin and multi-Galerkin methods and their iterated versions to solve the linear Fredholm integral equation of the second kind on the real line with a sufficiently smooth kernels, using Hermite polynomials as basis functions. We obtain optimal convergence results in iterated Galerkin method in weighted L2−norm. We also discuss multi-Galerkin methods and we obtain the superconvergence results in both multi-Galerkin and iterated multi-Galerkin methods. Numerical results are presented to confirm the theoretical results.