@Article{AAMM-7-472, author = {Yue , ChaoXiao , 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 = {2018}, volume = {7}, number = {4}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2013.m230}, url = {http://global-sci.org/intro/article_detail/aamm/12059.html} }