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A New Family of Difference Schemes for Space Fractional Advection Diffusion Equation

Published online by Cambridge University Press:  09 January 2017

Can Li*
Affiliation:
Department of Applied Mathematics, School of Sciences, Xi'an University of Technology, Xi'an, Shaanxi 710054, China
Weihua Deng*
Affiliation:
School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou, Gansu 730000, China
*
*Corresponding author. Email:[email protected] (C. Li), [email protected] (W. H. Deng)
*Corresponding author. Email:[email protected] (C. Li), [email protected] (W. H. Deng)
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Abstract

The second order weighted and shifted Grünwald difference (WSGD) operators are developed in [Tian, Zhou and Deng, Math. Comput., 84 (2015), pp. 1703–1727] to solve space fractional partial differential equations. Along this direction, we further design a new family of second order WSGD operators; by properly choosing the weighted parameters, they can be effectively used to discretize space (Riemann-Liouville) fractional derivatives. Based on the new second order WSGD operators, we derive a family of difference schemes for the space fractional advection diffusion equation. By von Neumann stability analysis, it is proved that the obtained schemes are unconditionally stable. Finally, extensive numerical experiments are performed to demonstrate the performance of the schemes and confirm the convergence orders.

Type
Research Article
Copyright
Copyright © Global-Science Press 2017 

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