Year: 2015
Author: Chao Yue, Aiguo Xiao, Hongliang Liu
Advances in Applied Mathematics and Mechanics, Vol. 7 (2015), Iss. 4 : pp. 472–495
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 ($θ$,$\bar{p}$,$\bar{q}$)-algebraic stability of ARK methods for a class of stiff problems $K_{σ,τ}$ 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 $K_{σ,0}$ 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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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.2013.m230
Advances in Applied Mathematics and Mechanics, Vol. 7 (2015), Iss. 4 : pp. 472–495
Published online: 2015-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 24