Convergence of the matrix transformation method for the finite difference approximation of fractional order diffusion problems.

Autor:	Szekeres, Béla J.
Další autoři:	Izsák, Ferenc
Jazyk:	angličtina
Předmět:	články journal articles problém frakční difúze konečné rozdíly transformační metoda matice fractional diffusion problem finite differences matrix transformation method
Druh dokumentu:	Non-fiction
ISSN:	0862-7940
Abstrakt:	Abstract: 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 R² 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.
Databáze:	Katalog Knihovny AV ČR
Externí odkaz:	Plný text Full text from SpringerLink