We consider collocation-based Runge-Kutta-Nystrom methods with symmetric points and derive a three-stage method which results exact in phase for second order linear ODEs having a periodic or an oscillatory solution. We assume that the dominant frequency k can be estimated in advance; then the resulting method depends on the parameter theta = kh, where h is the stepsize. Due to its stability properties, the method is suitable to integrate systems which exhibits a moderate stiffness. The procedure can be easily generalized to derive phase-fitted RKN methods with an arbitrary high order.

A phase-fitted collocation-base Runge-Kutta-Nystrom method

PATERNOSTER, Beatrice
2000-01-01

Abstract

We consider collocation-based Runge-Kutta-Nystrom methods with symmetric points and derive a three-stage method which results exact in phase for second order linear ODEs having a periodic or an oscillatory solution. We assume that the dominant frequency k can be estimated in advance; then the resulting method depends on the parameter theta = kh, where h is the stepsize. Due to its stability properties, the method is suitable to integrate systems which exhibits a moderate stiffness. The procedure can be easily generalized to derive phase-fitted RKN methods with an arbitrary high order.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/1000195
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