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.
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页码：472 / 495
页数：24
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