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

Published online by Cambridge University Press:  29 May 2015

Chao Yue
Affiliation:
School of Mathematics and Computational Science & Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Hunan 411105, China School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China
Aiguo Xiao*
Affiliation:
School of Mathematics and Computational Science & Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Hunan 411105, China
Hongliang Liu
Affiliation:
School of Mathematics and Computational Science & Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Hunan 411105, China
*
*Corresponding author. Email: xag@xtu.edu.cn (A. G. Xiao)
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Abstract

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 -algebraic stability of ARK methods for a class of stiff problems Kστ 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 Kσ,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.

Type
Research Article
Copyright
Copyright © Global-Science Press 2015 

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