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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.

MSC:

65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
65L05 Numerical methods for initial value problems involving ordinary differential equations
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References:

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