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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2022, Volume 505, Pages 14–18
DOI: https://doi.org/10.31857/S2686954322040178
(Mi danma270)
 

MATHEMATICS

On numerical solution of a first kind integral equation with a weak singularity in the kernel on a closed surface

S. I. Smagin

Computing Center, Khabarovsk Federal Research Centre, Far Eastern Branch, Russian Academy of Sciences, Khabarovsk, Russia
References:
Abstract: A direct method (self-regularization method) for the numerical solution of a weakly singular integral equation of the first kind on a closed surface is considered. This equation is an integral formulation of the internal and external three-dimensional Dirichlet problems for the Laplace equation if their solutions are sought in the form of a single-layer potential. It is approximated by a system of linear algebraic equations, which is solved numerically. In this case, a new method of averaging the kernel of the integral operator is used. It preserves the conditional correctness of the discretized problem and significantly increases the rate of convergence of its solution to the exact solution of the integral equation.
Keywords: integral equation, operator, method, averaging, approximation, numerical solution.
Funding agency Grant number
Russian Foundation for Basic Research 20-01-00450
This work was supported by the Russian Foundation for Basic Research, project no. 20-01-00450.
Received: 09.12.2021
Revised: 11.04.2022
Accepted: 02.06.2022
English version:
Doklady Mathematics, 2022, Volume 106, Issue 1, Pages 220–224
DOI: https://doi.org/10.1134/S1064562422040172
Bibliographic databases:
Document Type: Article
UDC: 519.642.3
Language: Russian
Citation: S. I. Smagin, “On numerical solution of a first kind integral equation with a weak singularity in the kernel on a closed surface”, Dokl. RAN. Math. Inf. Proc. Upr., 505 (2022), 14–18; Dokl. Math., 106:1 (2022), 220–224
Citation in format AMSBIB
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\by S.~I.~Smagin
\paper On numerical solution of a first kind integral equation with a weak singularity in the kernel on a closed surface
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2022
\vol 505
\pages 14--18
\mathnet{http://mi.mathnet.ru/danma270}
\crossref{https://doi.org/10.31857/S2686954322040178}
\elib{https://elibrary.ru/item.asp?id=49344490}
\transl
\jour Dokl. Math.
\yr 2022
\vol 106
\issue 1
\pages 220--224
\crossref{https://doi.org/10.1134/S1064562422040172}
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