Nonlinear Stability and B-convergence of Additive Runge-Kutta Methods for Nonlinear Stiff Problems (Advances in Applied Mathematics and Mechanics, 2018)
In this paper, we are devoted to nonlinear stability and B-convergence ofadditive 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 stiffproblems $K_{σ,τ}$ is introduced, and it is proven that this stability implies some contractiveproperties of the ARK methods. Some results on optimal B-convergence of ARKmethods for $K_{σ,0}$ are given. These new results extend the existing ones of RK methodsand ARK methods in the references. Numerical examples test the correctness of ourtheoretical analysis.