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A zero-dissipative Runge-Kutta-Nyström method with minimal phase-lag. (English) Zbl 1192.65105
Summary: An explicit Runge-Kutta-Nyström (RKN) method is developed for solving second-order differential equations of the form $q^{\prime\prime}=f(t,q)$ where the solutions are oscillatory. The method has zero-dissipation with minimal phase-lag at a cost of three-function evaluations per step of integration. Numerical comparisons with RKN3HS, RKN3V, RKN4G, and RKN4C methods show the precision and effectiveness of the method developed.

##### MSC:
 65L06 Multistep, Runge-Kutta, and extrapolation methods 65L05 Initial value problems for ODE (numerical methods) 34A34 Nonlinear ODE and systems, general 34C10 Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
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##### References:
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