Fourth order finite difference schemes for time–space fractional sub-diffusion equations. (March 2016)

• Record Type: Journal Article
• Authors: Pang, Hong-Kui; Sun, Hai-Wei
• Is Part Of: Computers & mathematics with applications. Volume 71:issue 6(2016)
• Page Start: 1287
• Page End: 1302
• Publication Date: 2016-03
• Subjects: Time–space fractional sub-diffusion equations -- Fractional derivative -- Fourth order finite-difference approximation -- L1 approximation -- Stability -- Convergence; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2016.02.011
• Languages: English
• ISSNs: 0898-1221

Abstract

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.