Compact ADI method for solving two-dimensional Riesz space fractional diffusion equation

Abstract: 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.