Fourth order finite difference schemes for time–space fractional sub-diffusion equations. (March 2016) - Pang, Hong-Kui; Sun, Hai-Wei
Abstract: In this paper, we devote to the study of high order finite difference schemes for one- and two-dimensional time–space fractional sub-diffusion equations. A fourth order finite difference scheme is invoked for the spatial fractional derivatives, and the L 1 approximation is applied to the temporal fractional parts. For the two-dimensional case, an alternating direction implicit scheme based on L 1 approximation is proposed. The stability and convergence of the proposed methods are studied. Numerical experiments are performed to verify the effectiveness and accuracy of the proposed difference schemes.