Geodesic
Multipole expansion of the fundamental solution of a fractional degree of the Laplace operator
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the XVII All-Russian Youth School-Conference «Lobachevsky Readings-2018», November 23-28, 2018, Kazan. Part 2, Tome 176 (2020), pp. 26-33

Voir la notice de l'article provenant de la source Math-Net.Ru

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, fast multipole method, numerical algorithm.
Mots-clés : multipole expansion 
@article{INTO_2020_176_a2,
     author = {N. S. Belevtsov and S. Yu. Lukashchuk},
     title = {Multipole expansion of the fundamental solution of a fractional degree of the {Laplace} operator},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {26--33},
     publisher = {mathdoc},
     volume = {176},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2020_176_a2/}
}
TY  - JOUR
AU  - N. S. Belevtsov
AU  - S. Yu. Lukashchuk
TI  - Multipole expansion of the fundamental solution of a fractional degree of the Laplace operator
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2020
SP  - 26
EP  - 33
VL  - 176
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2020_176_a2/
LA  - ru
ID  - INTO_2020_176_a2
ER  - 
%0 Journal Article
%A N. S. Belevtsov
%A S. Yu. Lukashchuk
%T Multipole expansion of the fundamental solution of a fractional degree of the Laplace operator
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2020
%P 26-33
%V 176
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2020_176_a2/
%G ru
%F INTO_2020_176_a2
N. S. Belevtsov; S. Yu. Lukashchuk. Multipole expansion of the fundamental solution of a fractional degree of the Laplace operator. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the XVII All-Russian Youth School-Conference «Lobachevsky Readings-2018», November 23-28, 2018, Kazan. Part 2, Tome 176 (2020), pp. 26-33. http://geodesic.mathdoc.fr/item/INTO_2020_176_a2/