Three-Point Combined Compact Alternating Direction Implicit Difference Schemes for Two-Dimensional Time-Fractional Advection-Diffusion Equations. (22nd January 2015)

• Record Type: Journal Article
• Authors: Gao, Guang-Hua; Sun, Hai-Wei
• Is Part Of: Communications in computational physics. Volume 17:Number 2(2015:Feb.)
• Page Start: 487
• Page End: 509
• Publication Date: 2015-01-22
• Subjects: 65M06, -- 65M12, -- 65N06, -- 65N12; Time-fractional advection-diffusion equations, -- combined compact difference (CCD) scheme, -- ADI, -- stability, -- Fourier analysis; Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.180314.010914a
• Languages: English
• ISSNs: 1815-2406

Abstract

Abstract: This paper is devoted to the discussion of numerical methods for solving two-dimensional time-fractional advection-diffusion equations. Two different three-point combined compact alternating direction implicit (CC-ADI) schemes are proposed and then, the original schemes for solving the two-dimensional problems are divided into two separate one-dimensional cases. Local truncation errors are analyzed and the unconditional stabilities of the obtained schemes are investigated by Fourier analysis method. Numerical experiments show the effectiveness and the spatial higher-order accuracy of the proposed methods.