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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2024, Volume 64, Number 2, Pages 253–262
DOI: https://doi.org/10.31857/S0044466924020064 (Mi zvmmf11703) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Partial Differential Equations

Explicit numerically implementable formulas for Poincaré–Steklov operators

A. S. Demidova, A. S. Samokhinb

a Lomonosov Moscow State University, 119991, Moscow, Russia
b Institute of Control Sciences, Russian Academy of Sciences, 117997, Moscow, Russia
Full-text PDF Citations (1)
DOI: https://doi.org/10.31857/S0044466924020064
Abstract: The paper presents explicit numerically implementable formulas for the Poincaré–Steklov operators, such as the Dirichlet–Neumann, Dirichlet–Robin, Robin1–Robin2, and Grinberg–Mayergoiz operators, related to the two-dimensional Laplace equation. These formulas are based on the lemma about a univalent isometric mapping of a closed analytic curve onto a circle. Numerical results for domains with very complex geometries were obtained for several test harmonic functions for the Dirichlet–Neumann and Dirichlet–Robin operators.
Key words: Poincaré–Steklov operators, univalent isometric mapping of an analytic curve, explicit numerically implementable formulas.
Received: 17.04.2023
Revised: 09.09.2023
Accepted: 20.10.2023
English version:
Computational Mathematics and Mathematical Physics, 2024, Volume 64, Issue 2, Pages 237–247
DOI: https://doi.org/10.1134/S0965542524020040
Bibliographic databases:
Document Type: Article
UDC: 519.63
Language: Russian
Citation: A. S. Demidov, A. S. Samokhin, “Explicit numerically implementable formulas for Poincaré–Steklov operators”, Zh. Vychisl. Mat. Mat. Fiz., 64:2 (2024), 253–262; Comput. Math. Math. Phys., 64:2 (2024), 237–247
Citation in format AMSBIB
\Bibitem{DemSam24}
\by A.~S.~Demidov, A.~S.~Samokhin
\paper Explicit numerically implementable formulas for Poincar\'e--Steklov operators
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2024
\vol 64
\issue 2
\pages 253--262
\mathnet{http://mi.mathnet.ru/zvmmf11703}
\crossref{https://doi.org/10.31857/S0044466924020064}
\elib{https://elibrary.ru/item.asp?id=71544520}
\transl
\jour Comput. Math. Math. Phys.
\yr 2024
\vol 64
\issue 2
\pages 237--247
\crossref{https://doi.org/10.1134/S0965542524020040}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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