Orthosymplectic integration of linear Hamiltonian systems
type: Item
instance of: scholarly article
title: Orthosymplectic integration of linear Hamiltonian systems
zbMATH Open document ID: 0880.65053
author: E. Van Vleck
author: Benedict Leimkuhler
published in: Numerische Mathematik
publication date: 1997-08-18T00:00:00Z
review text: A continuous, orthogonal and symplectic factorization procedure for integrating unstable linear Hamiltonian systems is presented. The method is based on the development of an orthogonal, symplectic change of variables to block triangular Hamiltonian form. Integration is thus carried out within the class of linear Hamiltonian systems. Use of an appropriate timestepping strategy ensures that the symplectic pairing of eigenvalues is automatically preserved. For long-term integrations, which are necessary in the calculation of Lyapunov exponents, the properties of such a symplectic framework can be expected to yield improved estimates. The method is illustrated and compared with other techniques by means of numerical experiments on some equations.
reviewed by: Zbigniew Dżygadło
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 37-XX
Mathematics Subject Classification ID: 65L07
Mathematics Subject Classification ID: 34D08
zbMATH DE Number: 1049545
zbMATH Keywords: orthosymplectic integration
zbMATH Keywords: numerical examples
zbMATH Keywords: unstable linear Hamiltonian systems
zbMATH Keywords: timestepping
zbMATH Keywords: long-term integrations
zbMATH Keywords: Lyapunov exponents
MaRDI profile type: Publication
full work available at URL: s002110050286
OpenAlex ID: W2038124303
DOI: 10.1007/S002110050286
description: scientific article; zbMATH DE number 1049545