Volume 26, Issue 4
A Note on Richardson Extrapolation of Galerkin Methods for Eigenvalue Problems of Fredholm Integral Equations

Qiumei Huang & Yidu Yang

DOI:

J. Comp. Math., 26 (2008), pp. 598-612

Published online: 2008-08

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  • 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.

  • Keywords

Fredholm integral equations Semi-simple eigenvalues Asymptotic expansion Galerkin method Richardson extrapolation Sloan iteration

  • AMS Subject Headings

65N25 65N30 65R20.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-26-598, author = {}, title = {A Note on Richardson Extrapolation of Galerkin Methods for Eigenvalue Problems of Fredholm Integral Equations}, journal = {Journal of Computational Mathematics}, year = {2008}, volume = {26}, number = {4}, pages = {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.}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8644.html} }
TY - JOUR T1 - A Note on Richardson Extrapolation of Galerkin Methods for Eigenvalue Problems of Fredholm Integral Equations JO - Journal of Computational Mathematics VL - 4 SP - 598 EP - 612 PY - 2008 DA - 2008/08 SN - 26 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8644.html KW - Fredholm integral equations KW - Semi-simple eigenvalues KW - Asymptotic expansion KW - Galerkin method KW - Richardson extrapolation KW - Sloan iteration AB - 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.
Qiumei Huang & Yidu Yang. (1970). A Note on Richardson Extrapolation of Galerkin Methods for Eigenvalue Problems of Fredholm Integral Equations. Journal of Computational Mathematics. 26 (4). 598-612. doi:
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