Journal
MATHEMATICS OF COMPUTATION
Volume 84, Issue 294, Pages 1703-1727Publisher
AMER MATHEMATICAL SOC
DOI: 10.1090/S0025-5718-2015-02917-2
Keywords
Riemann-Liouville fractional derivative; Fractional diffusion equation; Weighted and shifted Grunwald difference (WSGD) operator
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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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A class of second order approximations, called the weighted and shifted Grunwald difference (WSGD) operators, are proposed for Riemann-Liouville fractional derivatives, with their effective applications to numerically solving space fractional diffusion equations in one and two dimensions. The stability and convergence of our difference schemes for space fractional diffusion equations with constant coefficients in one and two dimensions are theoretically established. Several numerical examples are implemented to test the efficiency of the numerical schemes and confirm the convergence order, and the numerical results for variable coefficients problem are also presented.
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