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.

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