A Note on Richardson Extrapolation of Galerkin Methods for Eigenvalue Problems of Fredholm Integral Equations
Year: 2008
Journal of Computational Mathematics, Vol. 26 (2008), Iss. 4 : pp. 598–612
Abstract
In this paper, we introduce a new extrapolation formula by combining Richardson extrapolation and Sloan iteration algorithms. Using this extrapolation formula, we obtain some asymptotic expansions of the Galerkin finite element method for semi-simple eigenvalue problems of Fredholm integral equations of the second kind and improve the accuracy of the numerical approximations of the corresponding eigenvalues. Some numerical experiments are carried out to demonstrate the effectiveness of our new method and to confirm our theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2008-JCM-8644
Journal of Computational Mathematics, Vol. 26 (2008), Iss. 4 : pp. 598–612
Published online: 2008-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Fredholm integral equations Semi-simple eigenvalues Asymptotic expansion Galerkin method Richardson extrapolation Sloan iteration.