A phase-fitted collocation-based Runge-Kutta-Nyström method
type: Item
instance of: scholarly article
title: A phase-fitted collocation-based Runge-Kutta-Nyström method
zbMATH Open document ID: 0979.65063
DOI: 10.1016/S0168-9274(99)00143-9
published in: Applied Numerical Mathematics
publication date: 2002-02-10T00:00:00Z
review text: The author is concerned with the particular class of second order ordinary differential systems \[ y'' (t) = f(t, y(t)) \] with \( y(t), f(t, y(t)) \in \mathbb{R}^n \), initial conditions \[ y(t_0) = y_0, \qquad y'(t_0) = y'_0 \] and having a periodic or oscillatory solution. She derives collocation based Runge-Kutta-Nyström methods with symmetric points and identifies a three-stage method that is exact in phase for the linear case. The linear stability of the method is investigated by means of a symbolic-numerical package developed by \textit{M. Cafaro} and the author and available at the URL: \url{http://www.netlib.org/ode/symbolic}. As a consequence of its stability properties, the method is suitable for the numerical solution of systems which exhibit a moderate stiffness. Numerical experiments are reported at the end of the paper.
reviewed by: Riccardo Fazio
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L60
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 1557010
zbMATH Keywords: numerical experiments
zbMATH Keywords: Runge-Kutta-Nyström methods
zbMATH Keywords: systems
zbMATH Keywords: periodic or oscillatory solution
zbMATH Keywords: collocation
zbMATH Keywords: linear stability
author: Beatrice Paternoster
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1557010