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Runge-Kutta interpolants with minimal phase-lag. (English) Zbl 0791.65054
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 P. J. Van der Houwen and 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.
MSC:
65L06Multistep, Runge-Kutta, and extrapolation methods
65L05Initial value problems for ODE (numerical methods)
65L70Error bounds (numerical methods for ODE)
34A34Nonlinear ODE and systems, general