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Zbl 1192.65105
Senu, Norazak; Suleiman, Mohamed; Ismail, Fudziah; Othman, Mohamed
A zero-dissipative Runge-Kutta-Nyström method with minimal phase-lag. (English)
[J] Math. Probl. Eng. 2010, Article ID 591341, 15 p. (2010). ISSN 1024-123X; ISSN 1563-5147/e

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 2000:: *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, etc.

Keywords: oscillatory solution; Runge-Kutta-Nyström (RKN) method; second-order differential equations; zero-dissipation; minimal phase-lag; numerical comparisons

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Zentralblatt MATH Berlin [Germany]