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Zbl 0791.65054
Simos, T.E.
Runge-Kutta interpolants with minimal phase-lag.
(English)
[J] Comput. Math. Appl. 26, No.8, 43-49 (1993). ISSN 0898-1221

The author considers continuous extensions of Runge-Kutta methods which are intended for solving systems of ordinary differential equations with oscillatory solutions. For a given Runge-Kutta method of this type the phase-lag is defined and analysed. Based on the method of {\it P. J. Van der Houwen} and {\it B. P. Sommeijer} [SIAM J. Numer. Anal. 24, 595-617 (1987; Zbl 0624.65058)], an embedded Runge-Kutta method with phase-lag order 10 is constructed. Experiments show that using this embedded method for stepsize control gives comparable errors in both the interpolant and grid point values.
[G.Hall (Manchester)]
MSC 2000:
*65L06 Multistep, Runge-Kutta, and extrapolation methods
65L05 Initial value problems for ODE (numerical methods)
65L70 Error bounds (numerical methods for ODE)
34A34 Nonlinear ODE and systems, general

Keywords: Runge-Kutta methods; systems; oscillatory solutions; phase-lag; stepsize control

Citations: Zbl 0624.65058

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