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A class of second order difference approximations for solving space fractional diffusion equations


Authors: WenYi Tian, Han Zhou and Weihua Deng
Journal: Math. Comp. 84 (2015), 1703-1727
MSC (2010): Primary 26A33, 65L12, 65L20
Published electronically: January 6, 2015
MathSciNet review: 3335888
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Abstract: A class of second order approximations, called the weighted and shifted Grünwald 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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Additional Information

WenYi Tian
Affiliation: School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, People’s Republic of China
Email: twymath@gmail.com

Han Zhou
Affiliation: School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, People’s Republic of China
Email: zhouh2010@lzu.edu.cn

Weihua Deng
Affiliation: School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, People’s Republic of China
Address at time of publication: Department of Mathematics, Hong Kong Baptist University, Hong Kong, P.R. China – and – Department of Mathematics, Utrecht University, Utrecht, the Netherlands
Email: dengwh@lzu.edu.cn

DOI: https://doi.org/10.1090/S0025-5718-2015-02917-2
Keywords: Riemann-Liouville fractional derivative, Fractional diffusion equation, Weighted and shifted Gr\"unwald difference (WSGD) operator
Received by editor(s): January 28, 2012
Received by editor(s) in revised form: March 7, 2012, February 5, 2013, and November 14, 2013
Published electronically: January 6, 2015
Article copyright: © Copyright 2015 American Mathematical Society