Communications on Applied Mathematics and Computation ›› 2025, Vol. 7 ›› Issue (5): 2097-2119.doi: 10.1007/s42967-025-00491-5
Shi-Ping Tang1, Yu-Mei Huang2
收稿日期:2023-12-01
修回日期:2024-07-06
接受日期:2024-07-13
出版日期:2025-10-20
发布日期:2025-06-17
通讯作者:
Yu-Mei Huang,E-mail:huangym@lzu.edu.cn
E-mail:huangym@lzu.edu.cn
基金资助:Shi-Ping Tang1, Yu-Mei Huang2
Received:2023-12-01
Revised:2024-07-06
Accepted:2024-07-13
Online:2025-10-20
Published:2025-06-17
Contact:
Yu-Mei Huang,E-mail:huangym@lzu.edu.cn
E-mail:huangym@lzu.edu.cn
Supported by:摘要： In this paper, the backward Euler method and the shifted Grünwald-Letnikov formulas are utilized to discretize the space-fractional diffusion equations. The discretized result is a system of linear equations with a coefficient matrix being the sum of a diagonal matrix and a non-Hermitian Toeplitz matrix. By utilizing the Hermitian and skew-Hermitian splitting of the Toeplitz matrix, we develop a two-parameter DTHSS iteration method to solve the linear systems. The convergence is also discussed. A DTHSS- τ(α,γ) preconditioner is proposed and the preconditioned GMRES method combined with the proposed preconditioner is applied to solve the linear systems. The spectral analysis of the THSS- τ(α,γ) preconditioned matrix is provided. Experimental results demonstrate the effectiveness of the proposed methods in solving the space-fractional diffusion equations.
Shi-Ping Tang, Yu-Mei Huang. A DTHSS- τ Preconditioner for the Discretized Linear Systems of Space-Fractional Diffusion Equations[J]. Communications on Applied Mathematics and Computation, 2025, 7(5): 2097-2119.
Shi-Ping Tang, Yu-Mei Huang. A DTHSS- τ Preconditioner for the Discretized Linear Systems of Space-Fractional Diffusion Equations[J]. Communications on Applied Mathematics and Computation, 2025, 7(5): 2097-2119.
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