On the rate of convergence of projection-iterative methods for classes of weakly singular integral equations

Abstract

For classes of weakly singular integral equations of the second kind whose kernels have a power singularity, we find the optimal order of the rate of convergence of projection-iterative methods. Moreover, iterative methods of the Sokolov type are considered and, for weakly singular equations with differentiable coefficients, we present estimates of the rate of convergence of such methods.

This is a preview of subscription content, log in to check access.

References

  1. 1.

    B. G. Gabdulkhaev and V. E. Gorlov, “On the convergence of the polygonal method for solution of weakly singular integral equations,” in:Functional Analysis and Its Applications [in Russian], Kazan' University, Kazan' (1975), pp. 60–72.

    Google Scholar 

  2. 2.

    A. Yu. Luchka,Projection-Iterative Methods for Solution of Differential and Integral Equations [in Russian], Naukova Dumka, Kiev (1980).

    Google Scholar 

  3. 3.

    N. S. Kurpel',Projection-Iterative Methods for Solution of Operator Equations [in Russian], Naukova Dumka, Kiev (1968).

    Google Scholar 

  4. 4.

    G. I. Marchuk and V. I. Lebedev,Numerical Methods in the Theory of Neutron Transport [in Russian], Atomizdat, Moscow (1971).

    Google Scholar 

  5. 5.

    M. A. Sinenko, “On the relationship between the projection-iterative method and the KP-method for equations of the second kind,” in:Contemporary Problems in the Theory of Approximation and Complex Analysis, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1990), pp. 113–122.

    Google Scholar 

  6. 6.

    B. S. Kashin and A. A. Saakyan,Orthogonal Series [in Russian], Nauka, Moscow (1984).

    Google Scholar 

  7. 7.

    S. V. Pereverzev and S. G. Solodkii, “On optimization of direct methods of solving weakly singular integral equation,”J. Complexity,9, No. 2, 55–68 (1993).

    Google Scholar 

  8. 8.

    N. P. Korneichuk,Extremal Problems in the Theory of Approximation [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  9. 9.

    S. V. Pereverzev, “On the rate of convergence of methods of Sokolov type for integral equations with differentiable kernels,”Ukr. Mat. Zh.,37, No. 5, 605–609 (1985).

    Google Scholar 

  10. 10.

    L. V. Kantorovich and G. S. Akilov,Functional Analysis [in Russian], Nauka, Moscow (1977).

    Google Scholar 

Download references

Author information

Affiliations

Authors

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 4, pp. 498–505, April, 1995.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Pereverzev, S.V., Askarov, M. On the rate of convergence of projection-iterative methods for classes of weakly singular integral equations. Ukr Math J 47, 578–587 (1995). https://doi.org/10.1007/BF01056043

Download citation

Keywords

  • Integral Equation
  • Iterative Method
  • Singular Integral Equation
  • Optimal Order
  • Power Singularity