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

Part of: Real functions Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  09 January 2017

Can Li  and
Weihua Deng
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:mathlican@xaut.edu.cn (C. Li), dengwh@lzu.edu.cn (W. H. Deng)
*Corresponding author. Email:mathlican@xaut.edu.cn (C. Li), dengwh@lzu.edu.cn (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.

Keywords

Riemann-Liouville fractional derivativeWSGD operatorfractional advection diffusion equationfinite difference approximationstability

MSC classification

Secondary: 26A33: Fractional derivatives and integrals 65M06: Finite difference methods 65M12: Stability and convergence of numerical methods
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 2 , April 2017 , pp. 282 - 306
Copyright
Copyright © Global-Science Press 2017 

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