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

被引：0

作者：

Belevtsov N.S. ^{[1
]}

Lukashchuk S.Y. ^{[1
]}

机构：

[1] Ufa State Aviation Technical University, Ufa

来源：

Journal of Mathematical Sciences | 2023年 / 275卷 / 5期

关键词：

35J08; 35R11; fast multipole method; fractional Laplacian; fundamental solution; multipole expansion; numerical algorithm;

D O I：

10.1007/s10958-023-06696-4

中图分类号：

学科分类号：

摘要：

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. © 2023, Springer Nature Switzerland AG.

引用

页码：548 / 555

页数：7

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