Equilibria of Runge-Kutta methods (Q908662)

It is known that certain Runge-Kutta methods share the property that, in a constant-step implementation, if a solution trajectory converges to a bounded limit then it must be a fixed point of the underlying differential system. Such methods are called regular. In the present paper we provide a recursive test to check whether given method is regular. Moreover, by examining solution trajectories of linear equations, we prove that the order of an s-stage regular method may not exceed \(2[(s+2)/2]\) and that the maximal order of an A-stable regular Runge-Kutta method with an irreducible stability function is 4.