Doklady Mathematics

, Volume 100, Issue 2, pp 436–439 | Cite as

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

  • A. R. AlievEmail author
  • R. J. HeydarovEmail author


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


  1. 1.
    D. Colton and R. Kress, Integral Equation Methods in Scattering Theory (Wiley, New York, 1984).zbMATHGoogle Scholar
  2. 2.
    E. H. Khalilov, Diff. Equations 54 (4), 539–550 (2018).CrossRefGoogle Scholar
  3. 3.
    E. H. Khalilov and A. R. Aliev, Math. Methods Appl. Sci. 41 (16), 6921–6933 (2018).MathSciNetCrossRefGoogle Scholar
  4. 4.
    R. J. Heydarov, Proc. Inst. Math. Mech. Natl. Acad. Sci. Az. 42 (1), 3–9 (2016).MathSciNetGoogle Scholar
  5. 5.
    A. A. Kashirin and S. I. Smagin, Comput. Math. Math. Phys. 52 (8), 1173–1185 (2012).MathSciNetCrossRefGoogle Scholar
  6. 6.
    E. H. Khalilov, Comput. Math. Math. Phys. 56 (7), 1310–1318 (2016).MathSciNetCrossRefGoogle Scholar
  7. 7.
    P. J. Harris and K. Chen, J. Comput. Appl. Math. 156, 303–318 (2003).MathSciNetCrossRefGoogle Scholar
  8. 8.
    R. Kress, Math. Comput. Model. 15 (3–5), 229–243 (1991).CrossRefGoogle Scholar
  9. 9.
    V. S. Vladimirov, Equations of Mathematical Physics (Marcel Dekker, New York, 1971; Nauka, Moscow, 1976).Google Scholar
  10. 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].Google Scholar
  11. 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).MathSciNetzbMATHGoogle Scholar
  12. 12.
    R. J. Heydarov, Proc. Inst. Math. Mech. Natl. Acad. Sci. Az. 43 (1), 98–104 (2017).MathSciNetGoogle Scholar
  13. 13.
    G. M. Vainikko, Itogi Nauki Tekh. Ser. Mat. Anal. 16, 5–53 (1979).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Azerbaijan State Oil and Industry UniversityBakuAzerbaijan
  2. 2.Institute of Mathematics and Mechanics, Azerbaijan National Academy of SciencesBakuAzerbaijan
  3. 3.Ganja State UniversityGanjaAzerbaijan

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