A note on pseudo-symplectic Runge-Kutta methods
type: Item
instance of: scholarly article
title: A note on pseudo-symplectic Runge-Kutta methods
zbMATH Open document ID: 0918.65055
DOI: 10.1007/BF02510415
author: K. Appert
published in: BIT
publication date: 1999-04-27T00:00:00Z
review text: In a previous paper of the authors [ibid. 38, No. 3, 439-461 (1998; Zbl 0916.65084)] they introduced the so-called pseudo-symplectic Runge-Kutta methods of order \(r\) as methods of this type which preserve the symplectic form within \({\mathcal O}(h^r)\) terms. Further they proved that Runge-Kutta methods with algebraic order \(p\) and pseudo-symplectic order \(2p\), termed as methods of type \((p,2p)\), show a linear growth of the global error, and therefore can be useful for long term integrations. In this note the authors complete this research proving that there exist methods of the above type with \(p=4\) and six explicit stages and with \(p=5\) and eight explicit stages.
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L70
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 37-XX
zbMATH DE Number: 1251192
zbMATH Keywords: error bounds
zbMATH Keywords: Hamiltonian systems
zbMATH Keywords: pseudo-symplectic Runge-Kutta methods
reviewed by: Manuel Calvo
MaRDI profile type: Publication
cites work: Pseudo-symplectic Runge-Kutta methods
cites work: Q4725642
cites work: Solving Ordinary Differential Equations I
description: scientific article; zbMATH DE number 1251192