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Title: Convergence of the matrix transformation method for the finite difference approximation of fractional order diffusion problems (English)
Author: Szekeres, Béla J.
Author: Izsák, Ferenc
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 62
Issue: 1
Year: 2017
Pages: 15-36
Summary lang: English
Category: math
Summary: Numerical solution of fractional order diffusion problems with homogeneous Dirichlet boundary conditions is investigated on a square domain. An appropriate extension is applied to have a well-posed problem on $\mathbb {R}^2$ and the solution on the square is regarded as a localization. For the numerical approximation a finite difference method is applied combined with the matrix transformation method. Here the discrete fractional Laplacian is approximated with a matrix power instead of computing the complicated approximations of fractional order derivatives. The spatial convergence of this method is proved and demonstrated by some numerical experiments. (English)
Keyword: fractional diffusion problem
Keyword: finite differences
Keyword: matrix transformation method
MSC: 35R11
MSC: 65M06
MSC: 65M12
idZBL: Zbl 06738479
idMR: MR3615476
DOI: 10.21136/AM.2017.0385-15
Date available: 2017-01-25T15:43:38Z
Last updated: 2020-07-02
Stable URL:
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