A class of second order difference approximations for solving space fractional diffusion equations
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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.References
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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
- 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
- © Copyright 2015 American Mathematical Society
- Journal: Math. Comp. 84 (2015), 1703-1727
- MSC (2010): Primary 26A33, 65L12, 65L20
- DOI: https://doi.org/10.1090/S0025-5718-2015-02917-2
- MathSciNet review: 3335888