Three-point combined compact alternating direction implicit difference schemes for two-dimensional time- fractional advection-diffusion equations

This paper is devoted to the discussion of numerical methods for solving twodimensional 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. AMS subject classifications: 65M06, 65M12, 65N06, 65N12