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Zbl 1019.65050
Franco, J.M.
Runge-Kutta-Nyström methods adapted to the numerical integration of perturbed oscillators.
(English)
[J] Comput. Phys. Commun. 147, No.3, 770-787 (2002). ISSN 0010-4655

The paper deals with methods for the numerical integration of perturbed oscillators, i.e.\ nonstiff initial value problems of the form $y''(t) + \omega^2 y(t) = f(t, y(t), y'(t))$, $y(t_0) = y_0$, $y'(t_0) = y_0'$, where $f$ is assumed to be small in magnitude. For this purpose, the author derives explicit Runge-Kutta-Nyström methods of order up to 5. The order conditions are discussed in detail. Numerical examples are provided showing the efficiency of the algorithms.
[Kai Diethelm (Braunschweig)]
MSC 2000:
*65L06 Multistep, Runge-Kutta, and extrapolation methods
65L20 Stability of numerical methods for ODE
34A34 Nonlinear ODE and systems, general
65L05 Initial value problems for ODE (numerical methods)

Keywords: adapted Runge-Kutta-Nyström methods; perturbed oscillators; nonstiff initial value problems; order conditions; numerical examples

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