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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2022, Volume 62, Number 5, Pages 838–853
DOI: https://doi.org/10.31857/S0044466922050064 (Mi zvmmf11400) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Partial Differential Equations

Analysis of approximate solution for a class of systems of integral equations

E. H. Khalilov

Azerbaijan State Oil and Industry University, AZ 1010, Baku, Azerbaijan
Citations (1)
DOI: https://doi.org/10.31857/S0044466922050064
Abstract: The paper presents a substantiation of the collocation method for a system of integral equations for the field-matching boundary value problem for the Helmholtz equation in two-dimensional space. Quadrature formulas are constructed for the single and double layer potentials and the normal derivative of the single layer potential. At definite points, the system of integral equations is replaced by a system of algebraic equations, and the existence and uniqueness of a solution of the system of algebraic equations is shown. The convergence of the solution of a system of algebraic equations to the exact solution of a system of integral equations is proved, and the convergence rate of the method is found. In addition, a sequence is constructed that converges to the exact solution of the field-matching boundary value problem.
Key words: field-matching boundary value problem, Helmholtz equation, system of integral equations, single and double layer potentials, Hankel function quadrature formulas, collocation method.
Received: 20.08.2021
Revised: 20.08.2021
Accepted: 17.11.2021
English version:
Computational Mathematics and Mathematical Physics, 2022, Volume 62, Issue 5, Pages 811–826
DOI: https://doi.org/10.1134/S0965542522050062
Bibliographic databases:
Document Type: Article
UDC: 519.64
Language: Russian
Citation: E. H. Khalilov, “Analysis of approximate solution for a class of systems of integral equations”, Zh. Vychisl. Mat. Mat. Fiz., 62:5 (2022), 838–853; Comput. Math. Math. Phys., 62:5 (2022), 811–826
Citation in format AMSBIB
\Bibitem{Kha22}
\by E.~H.~Khalilov
\paper Analysis of approximate solution for a class of systems of integral equations
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2022
\vol 62
\issue 5
\pages 838--853
\mathnet{http://mi.mathnet.ru/zvmmf11400}
\crossref{https://doi.org/10.31857/S0044466922050064}
\elib{https://elibrary.ru/item.asp?id=48506055}
\transl
\jour Comput. Math. Math. Phys.
\yr 2022
\vol 62
\issue 5
\pages 811--826
\crossref{https://doi.org/10.1134/S0965542522050062}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85132143804}
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  • https://www.mathnet.ru/eng/zvmmf/v62/i5/p838
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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