Multipole Expansion of the Fundamental Solution of a Fractional Degree of the Laplace Operator

A multipole expansion of the fundamental solution of the fractional power 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 diffe...

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Published inJournal of mathematical sciences (New York, N.Y.) Vol. 275; no. 5; pp. 548 - 555
Main Authors Belevtsov, N. S., Lukashchuk, S. Yu
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.10.2023
Springer
Springer Nature B.V
Subjects
Algorithms
Laplace transforms
Mathematical analysis
Mathematics
Mathematics and Statistics
Multipoles
Numerical analysis
Poisson equation
Polynomials
numerical algorithm
fundamental solution
fractional Laplacian
35J08
35R11
fast multipole method
multipole expansion
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ISSN1072-3374
1573-8795
DOI10.1007/s10958-023-06696-4

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Summary:A multipole expansion of the fundamental solution of the fractional power 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.
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ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-023-06696-4