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Zbl 1037.65073
Franco, J. M.
A 5(3) pair of explicit ARKN methods for the numerical integration of perturbed oscillators.
(English)
[J] J. Comput. Appl. Math. 161, No. 2, 283-293 (2003). ISSN 0377-0427

Summary: A new embedded pair of explicit adapted Runge-Kutta-Nyström (ARKN) methods specially adapted to the numerical integration of perturbed oscillators is obtained. This pair depends on a parameter $\nu = \omega h > 0$ ($h$ is the integration step and $\omega$ is the dominant frequency), and it has four stages and algebraic orders five and three. The numerical experiments carried out show that the new pair is very competitive when it is compared with high-quality codes proposed in the scientific literature.
MSC 2000:
*65L06 Multistep, Runge-Kutta, and extrapolation methods
65L05 Initial value problems for ODE (numerical methods)
34A34 Nonlinear ODE and systems, general

Keywords: Adapted RKN methods; Embedded pairs; Oscillatory problems; adapted Runge-Kutta-Nyström methods; perturbed oscillators; numerical experiments

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