Skip to main content
SpringerLink
Log in

Approximate Solution of the Boundary Value Problem for the Helmholtz Equation with Impedance Condition

  • MATHEMATICS
  • Published:
Doklady Mathematics Aims and scope Submit manuscript

Abstract

The collocation method is justified for the integral equation of the impedance boundary value problem for the Helmholtz equation. A sequence is constructed that converges to the exact solution of this boundary value problem, and an error estimate is deduced.

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.

Similar content being viewed by others

REFERENCES

  1. D. Colton and R. Kress, Integral Equation Methods in Scattering Theory (Wiley, New York, 1984).

    MATH  Google Scholar 

  2. E. H. Khalilov, Diff. Equations 54 (4), 539–550 (2018).

    Article  Google Scholar 

  3. E. H. Khalilov and A. R. Aliev, Math. Methods Appl. Sci. 41 (16), 6921–6933 (2018).

    Article  MathSciNet  Google Scholar 

  4. R. J. Heydarov, Proc. Inst. Math. Mech. Natl. Acad. Sci. Az. 42 (1), 3–9 (2016).

    MathSciNet  Google Scholar 

  5. A. A. Kashirin and S. I. Smagin, Comput. Math. Math. Phys. 52 (8), 1173–1185 (2012).

    Article  MathSciNet  Google Scholar 

  6. E. H. Khalilov, Comput. Math. Math. Phys. 56 (7), 1310–1318 (2016).

    Article  MathSciNet  Google Scholar 

  7. P. J. Harris and K. Chen, J. Comput. Appl. Math. 156, 303–318 (2003).

    Article  MathSciNet  Google Scholar 

  8. R. Kress, Math. Comput. Model. 15 (3–5), 229–243 (1991).

    Article  Google Scholar 

  9. V. S. Vladimirov, Equations of Mathematical Physics (Marcel Dekker, New York, 1971; Nauka, Moscow, 1976).

  10. Yu. A. Kustov and B. I. Musaev, “Cubature formula for a two-dimensional singular integral and its applications” (Moscow, 1981); Available from VINITI, No. 4281-81 [in Russian].

  11. E. H. Khalilov, “Cubic formula for class of weakly singular surface integrals,” Proc. Inst. Math. Mech. Natl. Acad. Sci. Az. 39 (47), 69–76 (2013).

    MathSciNet  MATH  Google Scholar 

  12. R. J. Heydarov, Proc. Inst. Math. Mech. Natl. Acad. Sci. Az. 43 (1), 98–104 (2017).

    MathSciNet  Google Scholar 

  13. G. M. Vainikko, Itogi Nauki Tekh. Ser. Mat. Anal. 16, 5–53 (1979).

    Google Scholar 

Download references

Funding

This study was supported by the Azerbaijan State Oil and Industry University, project no. ADNSU-2018-1-01.

Author information

Authors and Affiliations

  1. Azerbaijan State Oil and Industry University, AZ1010, Baku, Azerbaijan

    A. R. Aliev & R. J. Heydarov

  2. Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, AZ1141, Baku, Azerbaijan

    A. R. Aliev

  3. Ganja State University, AZ2003, Ganja, Azerbaijan

    R. J. Heydarov

Authors
  1. A. R. Aliev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. J. Heydarov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to A. R. Aliev or R. J. Heydarov.

Additional information

Translated by N. Berestova

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Aliev, A.R., Heydarov, R.J. Approximate Solution of the Boundary Value Problem for the Helmholtz Equation with Impedance Condition. Dokl. Math. 100, 436–439 (2019). https://doi.org/10.1134/S1064562419050090

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1064562419050090

Search

Navigation