Nonlinear Stability and B-convergence of Additive Runge-Kutta Methods for Nonlinear Stiff Problems

被引：2

作者：

Yue, Chao ^{[1
,2
,3
]}

Xiao, Aiguo ^{[1
,2
]}

Liu, Hongliang ^{[1
,2
]}

机构：

[1] Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411105, Peoples R China

[2] Xiangtan Univ, Hunan Key Lab Computat & Simulat Sci & Engn, Xiangtan 411105, Peoples R China

[3] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China

来源：

ADVANCES IN APPLIED MATHEMATICS AND MECHANICS | 2015年 / 7卷 / 04期

关键词：

Stiff problem; additive Runge-Kuttamethod; implicit-explicitmethod; B-convergence; algebraic stability; SCHEMES; CONVECTION; ORDER;

D O I：

10.4208/aamm.2013.m230

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we are devoted to nonlinear stability and B-convergence of additive Runge-Kutta (ARK) methods for nonlinear stiff problems with multiple stiffness. The concept of (theta, p(-), q(-))-algebraic stability of ARK methods for a class of stiff problems K-sigma,K-tau is introduced, and it is proven that this stability implies some contractive properties of the ARK methods. Some results on optimal B-convergence of ARK methods for K-sigma,K-0 are given. These new results extend the existing ones of RK methods and ARK methods in the references. Numerical examples test the correctness of our theoretical analysis.

引用

页码：472 / 495

页数：24

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