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

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

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English version:
Computational Mathematics and Mathematical Physics, 2016, 56:7, 1310–1318

Bibliographic databases:

UDC: 519.633.6
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
\Bibitem{Kha16} \by E.~G.~Khalilov \paper Justification of the collocation method for the integral equation for a mixed boundary value problem for the Helmholtz equation \jour Zh. Vychisl. Mat. Mat. Fiz. \yr 2016 \vol 56 \issue 7 \pages 1340--1348 \mathnet{http://mi.mathnet.ru/zvmmf10432} \crossref{https://doi.org/10.7868/S0044466916070103} \elib{https://elibrary.ru/item.asp?id=26302240} \transl \jour Comput. Math. Math. Phys. \yr 2016 \vol 56 \issue 7 \pages 1310--1318 \crossref{https://doi.org/10.1134/S0965542516070101} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000381223400009} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84979747899} 

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This publication is cited in the following articles:
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2. 54, no. 4, 2018, 539–550
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
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
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
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
7. E. G. Khalilov, “Justification of the Collocation Method for a Class of Surface Integral Equations”, Math. Notes, 107:4 (2020), 663–678
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
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