BANDED M-MATRIX SPLITTING PRECONDITIONER FOR RIESZ SPACE FRACTIONAL REACTION-DISPERSION EQUATION

作     者：Shiping Tang Aili Yang Yujiang Wu Shiping Tang;Aili Yang;Yujiang Wu

作者机构：School of Mathematics and StatisticsLanzhou UniversityLanzhou 730000China School of Mathematics and StatisticsHainan Normal UniversityHaikou 570000China 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2024年第42卷第2期

页      面：372-389页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by the National Natural Science Foundation of China(Grant No.12161030) by the Hainan Provincial Natural Science Foundation of China(Grant No.121RC537) 

主　　题：Riesz space fractional equations Toeplitz matrix conjugate gradient method Incomplete Cholesky decomposition Banded M-matrix splitting 

摘      要：Based on the Crank-Nicolson and the weighted and shifted Grunwald 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 ***,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 *** overcome this deficiency,we further develop an effective banded M-matrix splitting preconditioner for the coefficient *** properties of this preconditioner together with its preconditioning effect are ***,Numerical examples are employed to test the robustness and the effectiveness of the proposed preconditioner.