Approximate compositions of a near identity map by multi-revolution Runge-Kutta methods
type: Item
instance of: scholarly article
title: Approximate compositions of a near identity map by multi-revolution Runge-Kutta methods
zbMATH Open document ID: 1067.65067
author: Laurent O. Jay
author: Luis Rández
author: Manuel Calvo
author: J. I. Montijano
published in: Numerische Mathematik
publication date: 2004-12-13T00:00:00Z
review text: Properties of multi-revolution Runge-Kutta methods applied to ordinary differential equations in a neighbourhood of nearly periodic orbits are analyzed. The basic idea of a multi-revolution method is to approximate the \(N\)th power \(\varphi^N\) of a near identity map \(\varphi\) by \(s\ll N\) evalutions of \(\varphi\) at suitable points. Using this approach multi-revolution methods can be reinterpreted as classical Runge-Kutta methods with a different step size. The authors give order conditions and order estimations. In addition, multi-revolution methods which preserve symplectic structures are described.
reviewed by: Johannes Schropp
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 65P10
Mathematics Subject Classification ID: 37M15
zbMATH DE Number: 2121821
zbMATH Keywords: periodic orbits
zbMATH Keywords: long-term integration
zbMATH Keywords: Runge-Kutta method
zbMATH Keywords: multi-revolution method
zbMATH Keywords: symplectic structures
MaRDI profile type: Publication
full work available at URL: s00211-004-0518-9
OpenAlex ID: W2063925453
DOI: 10.1007/S00211-004-0518-9
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description: scientific article; zbMATH DE number 2121821