117
Views
8
CrossRef citations to date
0
Altmetric
Original Articles

Numerical solution of Urysohn integral equations using the iterated collocation method

, &
Pages 143-154 | Received 30 Oct 2006, Accepted 27 Mar 2007, Published online: 31 Dec 2007

References

  • Kaneko , H. , Noren , R. D. and Padilla , P. A. 1997 . Superconvergence of the iterated collocation methods for Hammerstein equations . Journal of Computational and Applied Mathematics , 80 : 335 – 349 .
  • Kaneko , H. and Xu , Y. 1996 . Superconvergence of the iterated Galerkin methods for Hammerstein equations . SIAM Journal on Numerical Analysis , 33 : 1048 – 1064 .
  • Graham , I. , Joe , S. and Sloan , I. 1985 . Iterated Galerkin versus iterated collocation for integral equations of the second kind . IMA Journal of Numerical Analysis , 5 : 355 – 369 .
  • Joe , S. 1985 . Collocation methods using piecewise polynomials for second kind integral equations . Journal of Computational and Applied Mathematics , 12–13 : 391 – 400 .
  • Vainikko , G. 1967 . Perturbed Galerkin method and general theory of approximate methods for nonlinear equations . U.S.S.R. Computational Mathematics and Mathematical Physics , 7 : 723 – 751 . (English Translation of Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, Vol. 7, No. 4, pp. 1–41)
  • Kaneko , H. , Noren , R. and Xu , Y. 1992 . Numerical solutions for weakly singular Hammerstein equations and their superconvergence . Journal of Integral Equations and Applications , 4 : 391 – 407 .
  • Demko , S. 1976 . “ Splines approximation in Banach spaces ” . In Theory of Approximation with Applications , Edited by: Law , A. G. and Sahney , B. N. 146 – 154 . New York : Academic Press .
  • Devore , R. A. 1976 . “ Degree of approximation ” . In Approximation Theory , Edited by: Lorentz , G. G. , Chui , C. K. and Schumaker , L. L. Vol. 2 , 117 – 161 . New York : Academic Press .
  • Sloan , I. H. 1976 . Error analysis for a class of degenerate-kernel methods . Numerische Mathematik , 25 : 231 – 238 .
  • Sloan , I. H. 1976 . Improvement by iteration for compact operator equations . Mathematics of Computation , 30 : 758 – 764 .
  • Anselone , P. M. 1971 . Collectively Compact Operator Approximation Theory and Applications to Integral Equations , Englewood Cliffs, NJ : Prentice-Hall .
  • Atkinson , K. E. 1976 . A Survey of Numerical Methods for the Solution of Fredholm Integral Equations of the Second Kind , Philadelphia, PA : Society for Industrial and Applied Mathematics .
  • Atkinson , K. E. and Potra , F. A. 1987 . Projection and iterated projection methods for nonlinear integral equations . SIAM Journal on Numerical Analysis , 24 ( 6 ) : 1352 – 1373 .
  • Delves , L. M. and Mohamed , J. L. 1985 . Computational Methods for Integral Equations , Cambridge, , UK : Cambridge University Press .
  • Maleknejad , K. and Derili , H. 2006 . The collocation method for Hammerstein integral equation by Daubecies wavelets . Applied Mathematics and Computation , 172 : 846 – 864 .

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.