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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
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.
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
Linking options:
https://www.mathnet.ru/eng/into584 https://www.mathnet.ru/eng/into/v176/p26
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Abstract page: | 307 | Full-text PDF : | 207 | References: | 34 |
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