Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Interpolation correction for collocation solutions of Fredholm integro-differential equations

Author: Qiya Hu
Journal: Math. Comp. 67 (1998), 987-999
MSC (1991): Primary 65B10, 45D05, 65R20
MathSciNet review: 1464145
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we discuss the collocation method for a large class of Fredholm linear integro-differential equations. It will be shown that, when a certain higher order interpolation operation is added to the collocation solution of this equation, the new approximations will, under suitable assumptions, admit a multiterm error expansion in even powers of the step-size $h$. Based on this expansion, ideal multilevel correction results of this collocation solution are obtained.

References [Enhancements On Off] (What's this?)

  • 1. Carl de Boor and Blâir Swartz, Collocation at Gaussian points, SIAM J. Numer. Anal. 10 (1973), 582–606. MR 373328,
  • 2. J. Lei and X. Huang, The projection methods for operator equations, Wuhan University Press 1987.
  • 3. L. M. Delves and J. L. Mohamed, Computational methods for integral equations, Cambridge University Press, Cambridge, 1985. MR 837187
  • 4. Qi Ya Hu, Extrapolation of finite element solutions to a class of integro-differential equations, Natur. Sci. J. Xiangtan Univ. 14 (1992), no. 2, 28–34 (Chinese, with English and Chinese summaries). MR 1184341
  • 5. Q. Hu, Extrapolation for collocation solutions of Volterra integro-differential equations, Chinese J. Numer. Math. Appl. 18(1996), No.2, 28-37. CMP 97:08
  • 6. Q. Hu, Acceleration of Convergence for Galerkin method solutions to Fredholm Integro-differential Equations, Syst. Sci. and Math. 17(1997), 14-18. CMP 97:14
  • 7. Wolfgang Volk, The numerical solution of linear integro-differential equations by projection methods, J. Integral Equations 9 (1985), no. 1, suppl., 171–190. MR 792423
  • 8. Wolfgang Volk, The iterated Galerkin method for linear integro-differential equations, J. Comput. Appl. Math. 21 (1988), no. 1, 63–74. MR 923033,
  • 9. Ai Hui Zhou, An extrapolation method for finite element approximation of integro-differential equations with parameters, Systems Sci. Math. Sci. 3 (1990), no. 3, 278–285. MR 1182749
  • 10. Qi Ding Zhu and Li Qun Cao, Multilevel correction for the finite element method and the boundary element method, Natur. Sci. J. Xiangtan Univ. 14 (1992), no. 2, 1–5 (Chinese, with English and Chinese summaries). MR 1184335

Similar Articles

Retrieve articles in Mathematics of Computation with MSC (1991): 65B10, 45D05, 65R20

Retrieve articles in all journals with MSC (1991): 65B10, 45D05, 65R20

Additional Information

Qiya Hu
Affiliation: Institute of Mathematics, Chinese Academy of Science, Beijing 100080, China

Received by editor(s): January 10, 1995
Received by editor(s) in revised form: August 9, 1995, and October 22, 1996
Additional Notes: This work was partially supported by the National Science Foundation
Article copyright: © Copyright 1998 American Mathematical Society