Runge-Kutta-Nystrom Stability for aClass of General Linear Methods for y''=f(x,y)

Aim of this paper is to begin an investigation on the linear stability analysis of a class of General Linear Methods for special second order Ordinary Differential Equations, taking as a starting point a class of two-step Runge-Kutta-Nyström methods, which is obtained through a transformation of the two-step Runge-Kutta methods. We construct methods with one and two stages possessing the same stability properties of the indirect collocation Gauss-Legendre Runge-Kutta-Nyström methods, which are P-stable. Keywords: General linear methods, Runge-Kutta-Nystrom methods, linear stability, A-stability