Gauss-Runge-Kutta-Nyström methods
type: Item
instance of: scholarly article
title: Gauss-Runge-Kutta-Nyström methods
zbMATH Open document ID: 0904.65076
DOI: 10.1007/BF02510913
author: Christopher Burnton
author: Rudolf Scherer
published in: BIT
publication date: 1999-01-19T00:00:00Z
review text: The paper deals with an investigation of symplectic Runge-Kutta-Nyström (RKN) methods of the highest order. These methods are called Gauss-RKN methods as they are based on the Gauss-Legendre quadrature formulas. After a survey of RKN methods applied to Hamiltonian systems and a presentation of the conditions of symplecticness and symmetry, the authors prove the main results: Gauss-RKN methods are always symmetric, and symmetry is equivalent to symplecticness. Moreover, the authors show that for each stage number of all symplectic Gauss-RKN methods are given by a family of methods with one free parameter. In my opinion the paper is very important for further development of the theory of symplectic integrators and should be read by any specialist involved in study of numerical solutions of ordinary differential equations.
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 65L20
zbMATH DE Number: 1158317
zbMATH Keywords: Gauss method
zbMATH Keywords: symplectic Runge-Kutta-Nyström methods
zbMATH Keywords: Gauss-Legendre quadrature formulas
zbMATH Keywords: Hamiltonian systems
zbMATH Keywords: symmetry
reviewed by: Andrzej Marciniak
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1158317