A phase-fitted collocation-based Runge-Kutta-Nyström method
The author is concerned with the particular class of second order ordinary differential systems \[ y'' (t) = f(t, y(t)) \] with \( y(t), f(t, y(t)) \in \mathbb{R}^n \), initial conditions \[ y(t_0) = y_0, \qquad y'(t_0) = y'_0 \] and having a periodic or oscillatory solution. She derives collocation based Runge-Kutta-Nyström methods with symmetric points and identifies a three-stage method that is exact in phase for the linear case. The linear stability of the method is investigated by means of a symbolic-numerical package developed by \textit{M. Cafaro} and the author and available at the URL: \url{http://www.netlib.org/ode/symbolic}. As a consequence of its stability properties, the method is suitable for the numerical solution of systems which exhibit a moderate stiffness. Numerical experiments are reported at the end of the paper.
scientific article; zbMATH DE number 1557010
scientific article