A Banded Preconditioning Iteration Method for Time-Space Fractional Advection-Diffusion Equations. (24th January 2017) - Zeng, Min-Li; Zhang, Guo-Feng
Abstract : In this paper, we concentrate on the efficient solvers for the time-space fractional advection-diffusion equations. Firstly, the implicit finite difference schemes with the shifted Grünwald-Letnikov approximations for spatial fractional derivative and unshifted Grünwald-Letnikov approximations for time fractional derivative are employed to discretize time-space fractional advection-diffusion equations. The discretization results in a series of large dense linear systems. Then, a banded preconditioner is proposed and some theoretical properties for the preconditioning matrix are studied. Numerical implementations show that the banded preconditioner may lead to satisfactory experimental results when we choose appropriate bandwidth in the preconditioner.