Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2019, Volume 160, Pages 114–125 (Mi into430)  
Method of boundary integral equations with hypersingular integrals in boundary-value problems

A. V. Setukha

Lomonosov Moscow State University
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Abstract: In this paper, we formulate mathematical foundations of applications of boundary integral equations with strongly singular integrals understood in the sense of finite Hadamard value to numerical solution of certain boundary-value problems. We describe numerical schemes for solving boundary strongly singular equations based on quadrature formulas and the collocation method. Also, we make references to known results on the mathematical justification of the numerical methods described in the paper.
Keywords: hypersingular integral, boundary integral equation, boundary-value problem, numerical methods.
Bibliographic databases:
Document Type: Article
UDC: 517.9, 519.642
MSC: 30E25, 45E99, 65N38
Language: Russian
Citation: A. V. Setukha, “Method of boundary integral equations with hypersingular integrals in boundary-value problems”, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences ICMMAS-17, St. Petersburg Polytechnic University, July 24-28, 2017, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 160, VINITI, Moscow, 2019, 114–125
Citation in format AMSBIB
\Bibitem{Set19}
\by A.~V.~Setukha
\paper Method of boundary integral equations with hypersingular integrals in boundary-value problems
\inbook Proceedings of the International Conference on Mathematical Modelling in Applied Sciences ICMMAS-17,
St. Petersburg Polytechnic University, July 24-28, 2017
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2019
\vol 160
\pages 114--125
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into430}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3981836}
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