  In this paper, a compact alternating direction implicit (ADI) method has been
developed for solving two-dimensional Riesz space fractional diffusion
equation. The precision of the discretization method used in spatial directions
is twice the order of the corresponding fractional derivatives. It is proved
that the proposed method is unconditionally stable via the matrix analysis
method and the maximum error in achieving convergence is discussed. Several
numerical examples are considered aiming to demonstrate the validity and
applicability of the proposed technique.
