Journal
APPLIED NUMERICAL MATHEMATICS
Volume 90, Issue -, Pages 22-37Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.apnum.2014.11.007
Keywords
Fractional diffusion equations; Riemann-Liouville derivative; Weighted average methods; Von Neumann stability analysis
Categories
Funding
- CMUC (Portugal) through European program COMPETE/FEDER [PEst-C/MAT/UI0324/2013]
- FCT (Portugal) through European program COMPETE/FEDER [PEst-C/MAT/UI0324/2013]
- Program for New Century Excellent Talents in University [NCET-09-0438]
- National Natural Science Foundation of China [10801067, 11426174]
- Fundamental Research Funds for the Central Universities [lzujbky-2010-63]
- [UTAustin/MAT/066/2008]
- [PTDC/MAT-NAN/0593/2012]
- Fundação para a Ciência e a Tecnologia [PTDC/MAT-NAN/0593/2012] Funding Source: FCT
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A one dimensional fractional diffusion model with the Riemann-Liouville fractional derivative is studied. First, a second order discretization for this derivative is presented and then an unconditionally stable weighted average finite difference method is derived. The stability of this scheme is established by von Neumann analysis. Some numerical results are shown, which demonstrate the efficiency and convergence of the method. Additionally, some physical properties of this fractional diffusion system are simulated, which further confirm the effectiveness of our method. (C) 2014 IMACS. Published by Elsevier B.V. All rights reserved.
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