Abstract: In this paper, a Riesz space fractional advection-dispersion equation with fractional Robin boundary condition is considered. By applying the fractional central difference formula and the weighted and shifted Gru¨nwald-Letnikov formula, we derive a weighted implicit finite difference scheme with accuracy O（?t²+ h²）. The solvability,stability, and convergence of the proposed numerical scheme are proved. A numerical example is presented to confirm the accuracy and efficiency of the scheme. 

Key words: fractional advection-dispersion equation, Riesz fractional derivative, fractional , central difference, stability, convergence