We firstly develop the high-order numerical algorithms for the left and right Riemann-Liouville derivatives. Using these derived schemes, we can get high-order algorithms for the Riesz fractional derivative. Based on the approximate algorithm, we construct the numerical scheme for the space Riesz fractional diffusion equation, where a fourth-order scheme is proposed for the spacial Riesz derivative, and where a compact difference scheme is applied to approximating the first-order time derivative. It is shown that the difference scheme is unconditionally stable and convergent. Finally, numerical examples are provided which are in line with the theoretical analysis.
"High-Order Algorithms for Riesz Derivative and Their Applications ." Abstr. Appl. Anal. 2014 (SI58) 1 - 17, 2014. https://doi.org/10.1155/2014/653797