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Zbl 0624.65059
Dormand, J.R.; El-Mikkawy, M.E.A.; Prince, P.J.
Families of Runge-Kutta-Nyström formulae. (English)
[J] IMA J. Numer. Anal. 7, 235-250 (1987). ISSN 0272-4979; ISSN 1464-3642/e

The paper deals with the numerical integration of the initial value problem (1) $y''(x)=f(x,y(x))$; $y(x\sb 0)=y\sb 0$, $y'(x\sb 0)=y\sb 0'$. Embedded explicit Runge-Kutta-Nyström (RKN) methods are derived for the solution of (1) utilizing the fact that f does not depend on y'. A comparison (based on numerical tests) is made with the standard RKN methods.
[V.A.Velev]

MSC 2000:: *65L05 Initial value problems for ODE (numerical methods)
34A34 Nonlinear ODE and systems, general

Keywords: second-order system; non-stiff; embedded explicit Runge-Kutta-Nyström method; comparison; numerical tests

Cited in: Zbl 1185.65126 Zbl 1032.65073 Zbl 0785.65083

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