The order ofB-convergence of algebraically stable Runge-Kutta methods

In a previous paper it was shown that for a class of semi-linear problems many high order Runge-Kutta methods have order of optimalB-convergence one higher than the stage order. In this paper we show that for the more general class of nonlinear dissipative problems such as result holds only for a small class of Runge-Kutta methods and that such methods have at most classical order 3.