(untitled) (Advances in Applied Mathematics and Mechanics, 2018)
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,p,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.