Skip to main content
SpringerLink
Log in

On the Approximate Solution of Integro-Differential Equations with a Degenerate Coefficient

  • NUMERICAL METHODS
  • Published:
Differential Equations Aims and scope Submit manuscript

Abstract

We study a linear integro-differential equation of the third kind with a coefficient having power-order zeros. To solve this equation approximately in the space of generalized functions, we propose and justify a generalized version of the subdomain method based on special Kantorovich polynomials.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. Bart, G.R. and Warnock, R.L., Linear integral equations of the third kind,SIAM J. Math. Anal., 1973, vol. 4, no. 4, pp. 609–622.

    Article  MathSciNet  MATH  Google Scholar 

  2. Case, K.M. and Zweifel, P.F., Linear Transport Theory, Massachusetts–London–Ontario: Addison-Wesley Publ. Com., 1967.

    MATH  Google Scholar 

  3. Bzhikhatlov, Kh.G., Boundary value problem with a shift, Differ. Uravn., 1973, vol. 9, no. 1, pp. 162–165.

    MathSciNet  Google Scholar 

  4. Vekua, N.P., Integral equations of Fredholm type with an integral in the Hadamard sense, Tr. Tbilis. Mat. Inst., 1939, vol. 4, pp. 113–146.

    Google Scholar 

  5. Gabbasov, N.S., Theory of solvability of one class of integro-differential equations in the space of generalized functions, Differ. Uravn., 1999, vol. 35, no. 9, pp. 1216–1226.

    MathSciNet  Google Scholar 

  6. Gabbasov, N.S., New versions of spline methods for a class of integro-differential equations, Differ. Equations, 2001, vol. 37, no. 10, pp. 1449–1458.

    Article  MathSciNet  MATH  Google Scholar 

  7. Gabbasov, N.S., New version of the collocation method for integro-differential equations in a special case, Differ. Equations, 2008, vol. 44, no. 9, pp. 1289–1296.

    Article  MathSciNet  MATH  Google Scholar 

  8. Gabbasov, N.S., Direct methods for solving integro-differential equations in the singular case, Differ. Equations, 2016, vol. 52, no. 7, pp. 863–876.

    Article  MathSciNet  MATH  Google Scholar 

  9. Gabbasov, N.S., Order-optimal methods for integro-differential equations in the singular case, Differ. Equations, 2016, vol. 52, no. 9, pp. 1209–1218.

    Article  MathSciNet  MATH  Google Scholar 

  10. Gabbasov, N.S., Generalized collocation method for integro-differential equations in an exceptional case, Differ. Equations, 2018, vol. 54, no. 7, pp. 881–888.

    Article  MathSciNet  MATH  Google Scholar 

  11. Gabdulkhaev, B.G., Optimal’nye approksimatsii reshenii lineinykh zadach (Optimal Approximations to Solutions of Linear Problems), Kazan: Izd. Kazan. Univ., 1980.

    Google Scholar 

  12. Prössdorf, S., Singular integral equation with a symbol vanishing at finitely many points, Mat. Issled., 1972, vol. 7, no. 1, pp. 116–132.

    MathSciNet  Google Scholar 

  13. Gabbasov, N.S., Metody resheniya integral’nykh uravnenii Fredgol’ma v prostranstvakh obobshchennykh funktsii (Methods for Solving Integral Equations of Fredholm Type in the Spaces of Generalized Functions), Kazan: Izd. Kazan. Univ., 2006.

    Google Scholar 

  14. Gabbasov, N.S., A new direct method for solving integral equations of the first kind, Differ. Uravn., 1990, vol. 26, no. 12, pp. 2122–2127.

    MathSciNet  MATH  Google Scholar 

  15. Uzhdavinis, I.V., On the convergence of the subdomain type method,Differ. Uravn. Ikh Primen., 1971, no. 1, pp. 73–83.

  16. Edwards, R.E., Functional Analysis: Theory and Applications, New York–London: Holt, Rinehart and Winston, 1965. Translated under the title: Funktsional’nyi analiz, Moscow: Mir, 1969.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Naberezhnye Chelny Institute (Branch), Kazan (Volga Region) Federal University, Naberezhnye Chelny, Tatarstan, 423812, Russia

    N. S. Gabbasov

Authors
  1. N. S. Gabbasov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. S. Gabbasov.

Additional information

Translated by V. Potapchouck

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gabbasov, N.S. On the Approximate Solution of Integro-Differential Equations with a Degenerate Coefficient. Diff Equat 56, 1230–1236 (2020). https://doi.org/10.1134/S0012266120090128

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0012266120090128

Search

Navigation