Back to Search
Start Over
IRK-WSGD methods for space fractional diffusion equations.
- Source :
-
Applied Numerical Mathematics . Jun2021, Vol. 164, p222-244. 23p. - Publication Year :
- 2021
-
Abstract
- In this paper, we develop high order numerical schemes for the solution of the initial-boundary value problem of one-dimensional and two-dimensional space fractional diffusion equations of orders belonging to the interval (1 , 2). Firstly, certain weighted and shifted Grünwald difference (WSGD) operator is used to approximate space Riemann-Liouville fractional derivatives, resulting in a linear system of ordinary differential equations (ODEs). Then an implicit Runge-Kutta (IRK) method is applied to discretize the resulted ODEs. Thus, we get an IRK-WSGD method for the fractional diffusion equation. We prove that under certain hypotheses, the proposed IRK-WSGD schemes are stable and have temporally fourth order accuracy and spatially second/third order accuracy. Preconditioning for discretization linear systems is discussed. Numerical experiments are presented to illustrate the accuracy and efficiency of the method. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 01689274
- Volume :
- 164
- Database :
- Academic Search Index
- Journal :
- Applied Numerical Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 148432314
- Full Text :
- https://doi.org/10.1016/j.apnum.2020.11.012