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 Kσ,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 Kσ,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