Stability and convergence of 3-point WSGD schemes for two-sided space fractional advection-diffusion equations with variable coefficients.

In this paper, we consider high order numerical methods for the solution of the initial-boundary value problem of two-sided space fractional advection-diffusion equations (SFADEs). We use the Crank-Nicolson (CN) technique to discretize the temporal derivative, and apply 3-point weighted and shifted Grünwald difference (WSGD) operators to discretize the fractional derivatives of order α ∈ (1 , 2) and fractional derivatives of order β ∈ (0 , 1) , respectively. As a result, a new family of CN-WSGD schemes for SFADEs with temporally 2nd order and spatially j th order (j ≥ 2) accuracy are obtained. We then analyse the stability and the convergence of the numerical schemes. The extrapolated WSGD (EWSGD) operators are also discussed. Numerical examples are implemented to verify the theoretical results. [ABSTRACT FROM AUTHOR]