257
Views
6
CrossRef citations to date
0
Altmetric
Section B

Fast multilevel augmentation method for nonlinear integral equations

Pages 80-89 | Received 10 Jul 2010, Accepted 13 Sep 2011, Published online: 19 Oct 2011

References

  • Anselone , P. M. 1971 . Collectively Compact Operator Approximation Theory , Englewood Cliffs, NJ : Prentice-Hall .
  • Anselone , P. M. and Moore , R. H. 1964 . Approximate solutions of integral and operator equations . J. Math. Anal. Appl. , 9 : 268 – 277 .
  • Atkinson , K. E. 1973 . The numerical evaluation of fixed points for completed continuous operators . SIAM J. Numer. Anal. , 10 : 799 – 807 .
  • Atkinson , K. E. and Potra , F. A. 1987 . Projection and iterated projection methods for nonlinear integral equations . SIAM J. Numer. Anal. , 24 : 1352 – 1373 .
  • Chen , J. , Cheng , S. and Chen , Z. 2011 . Multilevel augmentation methods for solving the sine-Gordon equation . J. Math. Anal. Appl. , 375 : 706 – 724 .
  • Chen , Z. , Micchelli , C. A. and Xu , Y. 1997 . The Petrov–Galerkin methods for second kind integral equations II: Multiwavelet scheme . Adv. Comput. Math. , 7 : 199 – 233 .
  • Chen , Z. , Wu , B. and Xu , Y. 2009 . Fast multilevel augmentation methods for solving Hammerstein equations . SIAM J. Numer. Anal. , 47 : 2321 – 2346 .
  • Han , G. Q. 1994 . Asymptotic error expansion for the Nyström method for nonlinear Fredholm integral equations of the second kind . BIT , 34 : 254 – 261 .
  • Vainikko , G. M. 1967 . Perturbed Galerkin method and general theory of approximate methods for nonlinear equations . Ž. Vyčisl. Mat. i Mat. Fiz. , 7 : 732 – 751 . (English Transl., U.S.S.R. Comp. Math. and Math. Phys. 7 (1967), pp. 1–41.)
  • Weiss , R. 1974 . On the approximation of fixed points of nonlinear compact operators . SIAM J. Numer. Anal. , 11 : 550 – 553 .

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.