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Zh. Vychisl. Mat. Mat. Fiz., 2016, Volume 56, Number 7, Pages 1340–1348 (Mi zvmmf10432)  

This article is cited in 8 scientific papers (total in 8 papers)

Justification of the collocation method for the integral equation for a mixed boundary value problem for the Helmholtz equation

E. G. Khalilov

Azerbaijan State Oil and Industry University

Abstract: The surface integral equation for a spatial mixed boundary value problem for the Helmholtz equation is considered. At a set of chosen points, the equation is replaced with a system of algebraic equations, and the existence and uniqueness of the solution of this system is established. The convergence of the solutions of this system to the exact solution of the integral equation is proven, and the convergence rate of the method is determined.

Key words: collocation method, mixed problem, Helmholtz equation, method of surface integral equations.

DOI: https://doi.org/10.7868/S0044466916070103

Full text: PDF file (159 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2016, 56:7, 1310–1318

Bibliographic databases:

UDC: 519.633.6
Received: 18.03.2015
Revised: 07.10.2015

Citation: E. G. Khalilov, “Justification of the collocation method for the integral equation for a mixed boundary value problem for the Helmholtz equation”, Zh. Vychisl. Mat. Mat. Fiz., 56:7 (2016), 1340–1348; Comput. Math. Math. Phys., 56:7 (2016), 1310–1318

Citation in format AMSBIB
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\jour Zh. Vychisl. Mat. Mat. Fiz.
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\pages 1340--1348
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 69, no. 6, 2017, 955–969  crossref  mathscinet  isi
    2. 54, no. 4, 2018, 539–550  crossref  zmath  isi
    3. A. R. Aliev, R. J. Heydarov, “On appromximate solution of impedance boundary value problem for Helmholtz equation”, Azerbaijan J. Math., 7:2 (2017), 169–179  mathscinet  zmath  isi
    4. E. H. Khalilov, “On properties of the operator generated by the derivative of the acoustic potential of a simple layer”, J. Math. Sci., 231:2 (2018), 168–180  mathnet  crossref  crossref
    5. F. A. Abdullayev, E. H. Khalilov, “Constructive method for solving the external Neumann boundary value problem for the Helmholtz equation”, Proc. Inst. Math. Mech., 44:1 (2018), 62–69  isi
    6. E. H. Khalilov, A. R. Aliev, “Justification of a quadrature method for an integral equation to the external Neumann problem for the Helmholtz equation”, Math. Meth. Appl. Sci., 41:16 (2018), 6921–6933  crossref  isi  scopus
    7. E. G. Khalilov, “Justification of the Collocation Method for a Class of Surface Integral Equations”, Math. Notes, 107:4 (2020), 663–678  mathnet  crossref  crossref  mathscinet  isi  elib
    8. A. N. Tynda, K. A. Timoshenkov, “Primenenie metoda granichnykh integralnykh uravnenii k chislennomu resheniyu ellipticheskikh kraevykh zadach v $\mathbb{R}^3$”, Zhurnal SVMO, 22:3 (2020), 319–332  mathnet  crossref
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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