變系數(shù)反應(yīng)擴(kuò)散方程的雙參數(shù)分裂預(yù)處理方法

蔣沁紗　陳浩

四川師范大學(xué)學(xué)報(bào)（自然科學(xué)版）第46卷第5期

摘要：考慮一類空間變系數(shù)反應(yīng)擴(kuò)散方程的快速算法.針對(duì)二階改進(jìn)道格拉斯分裂時(shí)間離散所得線性代數(shù)系統(tǒng)，構(gòu)造一類雙參數(shù)交替分裂迭代方法.分析格式的收斂性，給出最優(yōu)參數(shù)的取值，并獲得相應(yīng)預(yù)處理子.數(shù)值結(jié)果驗(yàn)證新方法的有效性及相比單參數(shù)分裂迭代格式的優(yōu)越性.

關(guān)鍵詞：變系數(shù)反應(yīng)擴(kuò)散方程; 改進(jìn)道格拉斯分裂方法; 雙參數(shù); 交替分裂迭代方法; 預(yù)處理子

中圖分類號(hào)：O241.82; O241.6 文獻(xiàn)標(biāo)志碼：A 文章編號(hào)：1001-8395（2023）05-0638-08

1離散

2交替分裂迭代算法

3數(shù)值實(shí)驗(yàn)

4結(jié)束語

本文考慮了變系數(shù)反應(yīng)擴(kuò)散方程的快速算法，針對(duì)改進(jìn)道格拉斯分裂時(shí)間離散所得的線性代數(shù)系統(tǒng)，構(gòu)造了一類雙參數(shù)交替分裂迭代法，分析了其收斂性及最優(yōu)參數(shù)的取值.同時(shí)，將其與GMRES結(jié)合，構(gòu)造了一類預(yù)處理GMRES的方法，數(shù)值結(jié)果驗(yàn)證了新方法的收斂性.

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A Class of Alternating Splitting Preconditioning Method with Two Parameters

for Reaction-Diffusion Equations with Variable Coefficients in SpaceJIANG Qinsha，CHEN Hao（School of Mathematical Sciences， Chongqing Normal University， Chongqing 401331）

Abstract：This paper consider fast algorithms for solving a class of reaction-diffusion equations with variable coefficients. We propose an alternating splitting iterative method with two parameters for solving the linear algebraic systems resulting from the modified Douglas splitting discretization of the reaction-diffusion equations. We show that the proposed scheme is convergent and the optimal parameters are given. A splitting preconditioner is also derived for the linear system. Numerical results show that the proposed methods is effective and superior to the splitting iterative scheme with a single parameter.

Keywords：reaction-diffusion equation with variable coefficients; modified Douglas splitting method; two parameters; alternating splitting iteration method; preconditioner

2020 MSC：65F10; 65L06; 65N22

（編輯 余毅）