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 -

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.