The numerical solution of space-fractional differential equations is a hot issue in the field of science and engineering computing in recent years.In this paper,based on theτ-matrix and block α-circulant matrix,a new preconditioner for solving nonsymmetric all-at-once linear systems arising from the Riesz space-fractional diffusion equation which was discreted by Crank-Nicol son and fourth-order finite difference scheme was presented.Theoretical analysis showed that the preconditioned coefficient matrix can be decomposed into the sum of the unit matrix,a low rank matrix and a small norm matrix.Finally,numerical results confirm the effectiveness of the τ-matrix and block α-eirculant preconditioned GMRES method for solving the nonsymmetric all-at-once linear system.
维普
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