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On conjugate symplecticity of B-series integrators

Hairer, Ernst ; Zbinden, Christophe J.

In: Ima Journal of Numerical Analysis, 2013, vol. 33, no. 1, p. 57-79

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    Title
    • On conjugate symplecticity of B-series integrators
    Author
    • Hairer, Ernst
    • Zbinden, Christophe J.. Section de Mathématiques Université de Genève, 2-4 rue du Lièvre, CH-1211 Genève 4, Switzerland
    Document Type
    • Postprint
    Language
    • English
    Published in
    • Ima Journal of Numerical Analysis, 2013, vol. 33, no. 1, p. 57-79. Oxford University Press
    Other Version
    OAI-PMH Identifier
    • oai:doc.rero.ch:295922
    Summary
    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