A New Family of Difference Schemes for Space Fractional Advection Diffusion Equation (Advances in Applied Mathematics and Mechanics, 2018)
The second order weighted and shifted Grünwald difference (WSGD) operatorsare developed in [Tian, Zhou and Deng, Math. Comput., 84 (2015), pp. 1703–1727] to solve space fractional partial differential equations. Along this direction, wefurther design a new family of second order WSGD operators; by properly choosingthe 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 diffusionequation. By von Neumann stability analysis, it is proved that the obtained schemesare unconditionally stable. Finally, extensive numerical experiments are performed todemonstrate the performance of the schemes and confirm the convergence orders.