Geodesic
Convergence of the matrix transformation method for the finite difference approximation of fractional order diffusion problems
Applications of Mathematics, Tome 62 (2017) no. 1, pp. 15-36.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
DOI : 10.21136/AM.2017.0385-15
Classification : 35R11, 65M06, 65M12
Keywords: fractional diffusion problem; finite differences; matrix transformation method 
@article{10_21136_AM_2017_0385_15,
     author = {Szekeres, B\'ela J. and Izs\'ak, Ferenc},
     title = {Convergence of the matrix transformation method for the finite difference approximation of fractional order diffusion problems},
     journal = {Applications of Mathematics},
     pages = {15--36},
     publisher = {mathdoc},
     volume = {62},
     number = {1},
     year = {2017},
     doi = {10.21136/AM.2017.0385-15},
     mrnumber = {3615476},
     zbl = {06738479},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.2017.0385-15/}
}
TY  - JOUR
AU  - Szekeres, Béla J.
AU  - Izsák, Ferenc
TI  - Convergence of the matrix transformation method for the finite difference approximation of fractional order diffusion problems
JO  - Applications of Mathematics
PY  - 2017
SP  - 15
EP  - 36
VL  - 62
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.2017.0385-15/
DO  - 10.21136/AM.2017.0385-15
LA  - en
ID  - 10_21136_AM_2017_0385_15
ER  - 
%0 Journal Article
%A Szekeres, Béla J.
%A Izsák, Ferenc
%T Convergence of the matrix transformation method for the finite difference approximation of fractional order diffusion problems
%J Applications of Mathematics
%D 2017
%P 15-36
%V 62
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.2017.0385-15/
%R 10.21136/AM.2017.0385-15
%G en
%F 10_21136_AM_2017_0385_15
Szekeres, Béla J.; Izsák, Ferenc. Convergence of the matrix transformation method for the finite difference approximation of fractional order diffusion problems. Applications of Mathematics, Tome 62 (2017) no. 1, pp. 15-36. doi : 10.21136/AM.2017.0385-15. http://geodesic.mathdoc.fr/articles/10.21136/AM.2017.0385-15/

Cité par Sources :