@Article{AAMM-7-4,
author = {Yue, Chao and Xiao, Aiguo and Liu, Hongliang},
title = {Nonlinear Stability and B-convergence of Additive Runge-Kutta Methods for Nonlinear Stiff Problems},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2015},
volume = {7},
number = {4},
pages = {472--495},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.2013.m230},
url = {https://global-sci.com/article/73406/nonlinear-stability-and-b-convergence-of-additive-runge-kutta-methods-for-nonlinear-stiff-problems}
}