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On conjugate symplecticity of B-series integrators

Contributors

Hairer, Ernst; Zbinden, Christophe

Published in

IMA journal of numerical analysis, vol. 33, no. 1, p. 57-79

Publication date

2013

Abstract

The long-time integration of Hamiltonian differential equations requires special numerical methods. Symplectic integrators are an excellent choice, but there are situations (e.g., multistep schemes or energy-preserving methods), where symplecticity is not possible. It is then of interest to study whether the methods are conjugate symplectic and thus have the same long-time behaviour as symplectic methods. This question is addressed in this work for the class of B-series integrators. Algebraic criteria for conjugate symplecticity up to a certain order are presented in terms of the coefficients of the B-series. The effect of simplifying assumptions is investigated. These criteria are then applied to characterize the conjugate symplecticity of implicit Runge–Kutta methods (Lobatto IIIA and Lobatto IIIB) and of energy-preserving collocation methods.

Keywords

  • Conjugate symplecticity
  • Hamiltonian differential equations
  • Backward error analysis
  • Modified equations
  • B-series
  • Rooted trees
  • Simplifying assumptions
  • Lobatto IIIA methods
  • Lobatto IIIB methods
  • Energy-preserving integrators

UNIGE affiliation entities

Citation (ISO format)

HAIRER, Ernst, ZBINDEN, Christophe. On conjugate symplecticity of B-series integrators. In: IMA journal of numerical analysis, 2013, vol. 33, n° 1, p. 57–79. doi: 10.1093/imanum/drs010

Main files (1)

Article (Accepted version)

Identifiers

Additional URL for this publication

http://imajna.oxfordjournals.org/content/33/1/57.abstract

Journal ISSN

0272-4979
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336downloads

Technical informations

Creation

11/02/2013 10:53:00

First validation

11/02/2013 10:53:00

Update

14/03/2023 20:03:10

Status update

14/03/2023 20:03:10

Last indexation

30/10/2024 08:50:57
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