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 $L^2$-norms. We also obtain the superconvergence results in both multi-Galerkin and iterated multi-Galerkin methods, respectively, in weighted $L^2$-norm. Numerical results are presented to validate the theoretical results.

Keywords:

• Nonlinear integral equation
• Hammerstein integral equation
• Laguerre polynomials
• Galerkin method
• multi-Galerkin method
• superconvergence rates

2010 Mathematics Subject Classifications:

• 65R20
• 45B05
• 45G10

Disclosure statement

No potential conflict of interest was reported by the author(s).