Journal
JOURNAL OF SCIENTIFIC COMPUTING
Volume 56, Issue 1, Pages 45-66Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10915-012-9661-0
Keywords
Quasi-compact difference approximation; Riemann-Liouville fractional derivatives; Stability and convergence; Space fractional diffusion equation
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Funding
- Program for New Century Excellent Talents in University [NCET-09-0438]
- National Natural Science Foundation of China [10801067, 11271173]
- Fundamental Research Funds for the Central Universities [lzujbky-2010-63, lzujbky-2012-k26]
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In this paper, a compact difference operator, termed CWSGD, is designed to establish the quasi-compact finite difference schemes for approximating the space fractional diffusion equations in one and two dimensions. The method improves the spatial accuracy order of the weighted and shifted Grunwald difference (WSGD) scheme (Tian et al., arXiv:1201.5949) from 2 to 3. The numerical stability and convergence with respect to the discrete L (2) norm are theoretically analyzed. Numerical examples illustrate the effectiveness of the quasi-compact schemes and confirm the theoretical estimations.
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