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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2020, Volume 176, Pages 26–33
DOI: https://doi.org/10.36535/0233-6723-2020-176-26-33
(Mi into584)
 

Multipole expansion of the fundamental solution of a fractional degree of the Laplace operator

N. S. Belevtsov, S. Yu. Lukashchuk

Ufa State Aviation Technical University
References:
Abstract: A multipole expansion of the fundamental solution of the fractional degree of the Laplace operator is constructed in terms of the Gegenbauer polynomials. Based on the decomposition constructed and the idea of the fast multipole method, we propose a numerical algorithm for solving the fractional differential generalization of the Poisson equation in the two-dimensional and three-dimensional spaces.
Keywords: fractional Laplacian, fundamental solution, multipole expansion, fast multipole method, numerical algorithm.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 1.3103.2017/4.6
This work was supported by the Ministry of Education and Science of the Russian Federation within the framework of the state assignment No. 1.3103.2017/4.6 “Mathematical and computer modeling of filtration processes in inhomogeneous reservoirs of oil and gas fields based on the fractional differential approach.”
Bibliographic databases:
Document Type: Article
UDC: 517.968.72
MSC: 35R11, 35J08
Language: Russian
Citation: N. S. Belevtsov, S. Yu. Lukashchuk, “Multipole expansion of the fundamental solution of a fractional degree of the Laplace operator”, Proceedings of the XVII All-Russian Youth School-Conference «Lobachevsky Readings-2018», November 23-28, 2018, Kazan. Part 2, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 176, VINITI, Moscow, 2020, 26–33
Citation in format AMSBIB
\Bibitem{BelLuk20}
\by N.~S.~Belevtsov, S.~Yu.~Lukashchuk
\paper Multipole expansion of the fundamental solution of a fractional degree of the Laplace operator
\inbook Proceedings of the XVII All-Russian Youth School-Conference «Lobachevsky Readings-2018»,
November 23-28, 2018, Kazan. Part 2
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2020
\vol 176
\pages 26--33
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into584}
\crossref{https://doi.org/10.36535/0233-6723-2020-176-26-33}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4150679}
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    Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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