变系数里兹空间分数扩散方程的无条件收敛[公式省略]分裂迭代法

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2024-07-31 DOI:10.1016/j.aml.2024.109252

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引用次数: 0

摘要

在本文中，我们考虑了由 Riesz 空间分数扩散方程生成的离散线性系统的快速求解器。我们从系数矩阵中提取了一个标量矩阵、一个补偿矩阵和一个矩阵，并利用它们的总和构建了一类分裂迭代法。此外，我们还为共轭梯度法设计了一个前置条件器。理论分析表明，所提出的分裂迭代法是无条件收敛的，收敛率与步长无关。我们还提供了数值结果来证明所提迭代法的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Unconditionally convergent τ splitting iterative methods for variable coefficient Riesz space fractional diffusion equations

In this paper, we consider fast solvers for discrete linear systems generated by Riesz space fractional diffusion equations. We extract a scalar matrix, a compensation matrix, and a $τ$ matrix from the coefficient matrix, and use their sum to construct a class of $τ$ splitting iterative methods. Additionally, we design a preconditioner for the conjugate gradient method. Theoretical analyses show that the proposed $τ$ splitting iterative methods are unconditionally convergent with convergence rates independent of step-sizes. Numerical results are provided to demonstrate the effectiveness of the proposed iterative methods.

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来源期刊

Applied Mathematics Letters 数学-应用数学

CiteScore

7.70

自引率

5.40%

发文量

347

审稿时长

10 days

期刊介绍： The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.