Stability analysis of frequency and step length dependent Runge–Kutta–Nyström methods

We present a symbolic–numerical package to analyze the linear stability properties of Runge–Kutta–Nyström methods for y′′=f(x,y), which are suitable for ordinary differential equations having periodic or oscillatory solutions, having frequency and step length dependent parameters. As an example, we apply this analysis to a special class of numerical methods appeared in the literature, which are based on trigonometric polynomials.