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Runge-Kutta-Nyström methods adapted to the numerical integration of perturbed oscillators. (English) Zbl 1019.65050
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.

65L06Multistep, Runge-Kutta, and extrapolation methods
65L20Stability and convergence of numerical methods for ODE
34A34Nonlinear ODE and systems, general
65L05Initial value problems for ODE (numerical methods)
Full Text: DOI
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