118
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

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

Pages 1067-1086 | Received 19 Nov 2014, Accepted 09 Apr 2015, Published online: 27 Jul 2015

REFERENCES

  • M. Ahues , A. Largillier , and B. V. Limaye ( 2001 ). Spectral Computations for Bounded Operators . Chapman and Hall/CRC , Boca Raton , FL .
  • K. E. Atkinson and F. A. Potra ( 1987 ). Projection and iterated projection methods for nonlinear integral equations . SIAM J. Numer. Anal. 24 : 1352 – 1373 .
  • C. T. H. Baker ( 1971 ). The deferred approach to the limit for eigenvalues of integral equations . SIAM J. Numer. Anal. 8 : 1 – 10 .
  • C. T. H. Baker ( 1977 ). The Numerical Treatment of Integral Equations . Oxford University Press , Oxford .
  • F. Chatelin and R. Lebbar ( 1984 ). Superconvergence Results for the iterated projection method applied to a Fredholm integral equation of the second kind and the corresponding eigenvalue problem . J. Integral Equations Appl. 6 : 71 – 91 .
  • Q. Huang and Y. Yang ( 2008 ). A note on Richardson extrapolation of Galerkin methods of eigenvalue poblems of Fredholm integral equations . J. Computational Math. 26 : 598 – 612 .
  • R. P. Kulkarni ( 1997 ). Use of extrapolation for improving the order of convergence of eigenelement approximations . IMA J. Numer. Anal. 17 : 271 – 284 .
  • R. P. Kulkarni ( 2005 ). On improvement of the iterated Galerkin solution of the second kind integral equations . J. Numerical Mathematics 13 : 205 – 218 .
  • R. P. Kulkarni and A. S. Rane ( 2012 ). Asymptotic expansions for approximate solutions of Fredholm integral equations with Green's function type kernels . J. Integral Equations Appl. 24 : 39 – 79 .
  • R. P. Kulkarni and A. S. Rane (2012). Asymptotic expansions for approximate eigenvalues of integral operators with nonsmooth kernels. Numer. Funct. Anal. Optim. 33:415–440.
  • Q. Lin , I. H. Sloan , and R. Xie ( 1990 ). Extrapolation of the iterated-collocation method for integral equations of the second kind . SIAM J. Numer. Anal. 6 : 1535 – 1541 .
  • W. Mclean ( 1989 ). Asymptotic error expansions for numerical solution of integral equations . IMA J. Numer. Anal. 9 : 373 – 384 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.