Stability regions of one step mixed collocation methods for y″=f(x,y)

We analyze the linear stability properties of mixed collocation Runge-Kutta-Nyström (RKN) methods for the second order Ordinary Differential Equations y″=f(x,y). In particular we consider the influence of the collocation nodes on the stability region, analyzing in detail the case of frequency and step length dependent RKN methods obtained through mixed collocation which are based on Gauss, Radau and Lobatto nodes.