On invariant closed curves for one-step methods
type: Item
instance of: scholarly article
title: On invariant closed curves for one-step methods
zbMATH Open document ID: 0617.65082
DOI: 10.1007/BF01399697
author: Wolf-Jürgen Beyn
published in: Numerische Mathematik
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133187
review text: Autonomous differential equations \(x'=f(x)\) are considered which possess a hyperbolic closed orbit \(\gamma\). It is shown that the application of a one-step method (e.g. an explicit Runge-Kutta method) yields an invariant closed curve \(\gamma_ h\) for sufficiently small (constant) step size h. This closed curve converges for \(h\to 0\) to the periodic orbit of the system with the order of the method and it inherits the stability of the periodic orbit. Several numerical experiments confirm the theoretical results.
reviewed by: Ernst Hairer
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 37-XX
zbMATH DE Number: 4001369
zbMATH Keywords: Autonomous differential equations
zbMATH Keywords: hyperbolic closed orbit
zbMATH Keywords: one-step method
zbMATH Keywords: explicit Runge-Kutta method
zbMATH Keywords: periodic orbit
zbMATH Keywords: numerical experiments
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4001369