Abstract
The implicit finite difference scheme with the shifted Grüwald formula for discretizing the fractional diffusion equations (FDEs) often results in the ill-conditioned non-Hermitian Toeplitz systems. In the present paper, we consider to solve such Toeplitz systems by exploiting the preconditioned GMRES method. A k -step polynomial preconditioner is designed based on the circulant and skew-circulant splitting (CSCS) iteration method proposed by Ng (2003). Theoretical and experimental results involving numerical solutions of FDEs demonstrate that the proposed k -step preconditioner is efficient to accelerate the GMRES solver for non-Hermitian Toeplitz systems.
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