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Ukrainian Mathematical Journal

, Volume 45, Issue 12, pp 1907–1914 | Cite as

On the optimization of direct methods for solving fredholm integral equations of the second kind with infinitely smooth kernels

  • A. N. Urumbaev
Article
  • 29 Downloads

Abstract

We give a direct method, optimal inL2, for solving the Fredholm integral equation of the second kind with operators acting into the space of functions harmonic in a disk or into the space of functions that can be analytically extended to an infinite strip. The exact order of the error of this method is determined.

Keywords

Integral Equation Fredholm Integral Equation Exact Order Smooth Kernel Infinite Strip 
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References

  1. 1.
    S. V. Pereverzev and A. N. Urumbaev, “On optimal direct methods for solving Volterra equations in Hilbert spaces,”Mat. Zametki,52, No. 4, 74–84 (1992).Google Scholar
  2. 2.
    W. Ritz, “Über eine neue Methode zur Lösung gewisser Variationsprobleme der mathematischen Physik,”J. Reine Angew. Math,135, No. 1, 1–62 (1908).Google Scholar
  3. 3.
    S. V. Pereverzev, “On optimization of adaptive methods for approximate solving integral equations,”Dokl. Akad. Nauk SSSR,267, No. 6, 1304–1308 (1982).Google Scholar
  4. 4.
    S. Heinrich, “On the optimal error of degenerate kernel methods,”J. Integr. Equat.,9, No. 3, 251–256 (1985).Google Scholar
  5. 5.
    S. V. Pereverzev, “On optimization of methods for approximate solving integral equations with differentiable kernels,”Sib. Mat. Zh.,28, No. 3, 173–183 (1987).Google Scholar
  6. 6.
    S. V. Pereverzev and S. G. Solodkii, “On optimization of methods for approximate solving two-dimensional Fredholm equations of the second kind,”Ukr. Mat. Zh.,42, No. 8, 1077–1082 (1990).Google Scholar
  7. 7.
    S. G. Solodkii, “Optimization of adaptive direct methods for solving operator equations in a Hilbert space,”Ukr. Mat. Zh.,42, No. 1, 95–101 (1990).Google Scholar
  8. 8.
    J. H. Sloan, “Improvement by iteration for compact operator equations,”Math. Comp.,36, No. 136, 758–764 (1976).Google Scholar
  9. 9.
    L. V. Kantorovich and G. P. Akilov,Functional Analysis [in Russian], Nauka, Moscow (1977).Google Scholar
  10. 10.
    V. M. Tikhomirov,Some Problems in Approximation Theory [in Russian], Izd. Mosk. Univ., Moscow (1976).Google Scholar
  11. 11.
    S. N. Zaliznyak, Yu. I. Mel'nik, and Yu. K. Podlipenko, “On approximate solution of integral equations in potential theory,”Ukr. Mat. Zh.,33, No. 3, 385–391 (1981).Google Scholar
  12. 12.
    B. G. Gabdulkhaev,Optimal Approximations of Solutions of Linear Problems [in Russian], Izd. Kazan. Univ., Kazan' (1980).Google Scholar
  13. 13.
    B. G. Gabdulkhaev and G. D. Velev, “Best approximations of solutions of functional equations and optimization of numerical methods,” in:Proceedings of the International Conference on the Constructive Theory of Functions [in Russian], Publ. Bulg. Acad. Sci., Sofia (1984), pp. 18–26.Google Scholar

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • A. N. Urumbaev
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKiev

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