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-Nystrom 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.

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