| 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:
|
http://hdl.handle.net/10338.dmlcz/145987 |
| . |
| Reference:
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