Year: 2024
Author: Shiping Tang, Aili Yang, Yujiang Wu
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 2 : pp. 372–389
Abstract
Based on the Crank-Nicolson and the weighted and shifted Grünwald operators, we present an implicit difference scheme for the Riesz space fractional reaction-dispersion equations and also analyze the stability and the convergence of this implicit difference scheme. However, after estimating the condition number of the coefficient matrix of the discretized scheme, we find that this coefficient matrix is ill-conditioned when the spatial mesh-size is sufficiently small. To overcome this deficiency, we further develop an effective banded $M$-matrix splitting preconditioner for the coefficient matrix. Some properties of this preconditioner together with its preconditioning effect are discussed. Finally, Numerical examples are employed to test the robustness and the effectiveness of the proposed preconditioner.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2203-m2020-0192
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 2 : pp. 372–389
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Riesz space fractional equations Toeplitz matrix conjugate gradient method Incomplete Cholesky decomposition Banded $M$-matrix splitting.
Author Details
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https://doi.org/10.1007/s40314-024-02592-y [Citations: 0]