A Note on Asymptotic Expansions to Approximate Eigenvalues of Integral Operators with Green's Kernels using the Iterated Galerkin Method

Abstract

In this article, we consider approximation of eigenvalues of integral operators with Green's function-type kernels using the iterated Galerkin method. We obtain asymptotic expansions for approximate eigenvalues. The Richardson extrapolation is used to obtain eigenvalue approximations of higher order. A numerical example is considered in order to illustrate our theoretical results.

Keywords:

• Asymptotic expansion
• Fredholm integral operator
• Green's function-type kernels
• Iterated Galerkin method

Mathematics Subject Classification:

• 45B05
• 65R20

ACKNOWLEDGEMENTS

This work was done during a visit to the Institut Camille Jordan(ICJ), Universite Jean Monnet of Saint Etienne. The author would like to thank Prof. Rekha Kulkarni for carefully going through the article. The author also wishes to thank Prof. Mario Ahues and Prof. Laurence Grammont of Universite Jean Monnet for fruitful discussions.