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

  • Can Li (a1) and Weihua Deng (a2)

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.

Corresponding author
*Corresponding author. (C. Li), (W. H. Deng)
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[26] J. C.Strikwerda , Finite Difference Schemes and Partial Differential Equations, SIAM, 2004.

[28] J. W.Thomas , Numerical Partial Differential Equations: Finite Difference Methods, Springer New York, 1995.

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Advances in Applied Mathematics and Mechanics
  • ISSN: 2070-0733
  • EISSN: 2075-1354
  • URL: /core/journals/advances-in-applied-mathematics-and-mechanics
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