Three-Point Combined Compact Alternating Direction Implicit Difference Schemes for Two-Dimensional Time-Fractional Advection-Diffusion Equations (Communications in Computational Physics, 2020)
This paper is devoted to the discussion of numerical methods for solvingtwo-dimensional time-fractional advection-diffusion equations. Two different three-pointcombined compact alternating direction implicit (CC-ADI) schemes are proposedand then, the original schemes for solving the two-dimensional problems are dividedinto two separate one-dimensional cases. Local truncation errors are analyzed and theunconditional stabilities of the obtained schemes are investigated by Fourier analysismethod. Numerical experiments show the effectiveness and the spatial higher-orderaccuracy of the proposed methods.