  In this paper, a mixed high order finite difference scheme-Pad\'{e}
approximation method is applied to obtain numerical solution of the Riesz
fractional advection-dispersion equation. This method is based on the high
order finite difference scheme that derived from fractional centered difference
and Pad\'{e} approximation method for space and time integration, respectively.
The stability analysis of the proposed method is discussed via theoretical
matrix analysis. Numerical experiments are carried out to confirm the
theoretical results of the proposed method.
