A phase-fitted collocation-based Runge-Kutta-Nyström method. (English) Zbl 0979.65063

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 M. Cafaro and the author and available at the 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.


65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems


Zbl 0908.65071


Full Text: DOI


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