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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 '' =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:
65L06Multistep, Runge-Kutta, and extrapolation methods
65L05Initial value problems for ODE (numerical methods)
34A34Nonlinear ODE and systems, general
34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory