Stability analysis of frequency and step length dependent Runge-Kutta-Nystroem methods

摘要

We present a symbolic-numerical package to analyze the linear stability properties of Runge-Kutta-Nystroem 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.