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Global modified Hamiltonian for constrained symplectic integrators

Hairer, Ernst

In: Numerische Mathematik, 2003, vol. 95, no. 2, p. 325-336

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    Titre
    • Global modified Hamiltonian for constrained symplectic integrators
    Auteur
    • Hairer, Ernst. Dept. de Mathématiques, Université de Genève, CH-1211 Genève 24, Switzerland
    Type de document
    • Postprint
    Classification
    • Informatique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:317276
    Summary
    Summary.: We prove that the numerical solution of partitioned Runge-Kutta methods applied to constrained Hamiltonian systems (e.g., the Rattle algorithm or the Lobatto IIIA-IIIB pair) is formally equal to the exact solution of a constrained Hamiltonian system with a globally defined modified Hamiltonian. This property is essential for a better understanding of their longtime behaviour. As an illustration, the equations of motion of an unsymmetric top are solved using a parameterization with Euler parameters