TY - JOUR
T1 - Nonlinear Stability and B-convergence of Additive Runge-Kutta Methods for Nonlinear Stiff Problems
AU - Yue , Chao
AU - Xiao , Aiguo
AU - Liu , Hongliang
JO - Advances in Applied Mathematics and Mechanics
VL - 4
SP - 472
EP - 495
PY - 2018
DA - 2018/05
SN - 7
DO - http://doi.org/10.4208/aamm.2013.m230
UR - https://global-sci.org/intro/article_detail/aamm/12059.html
KW - 
AB - <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>