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Symmetric multistep methods for constrained Hamiltonian systems

Console, Paola ; Hairer, Ernst ; Lubich, Christian

In: Numerische Mathematik, 2013, vol. 124, no. 3, p. 517-539

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    Titel
    • Symmetric multistep methods for constrained Hamiltonian systems
    Autor
    • Console, Paola. Dept. de Mathématiques, Univ. de Genève, 1211, Genève 4, Switzerland
    • Hairer, Ernst. Dept. de Mathématiques, Univ. de Genève, 1211, Genève 4, Switzerland
    • Lubich, Christian. Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle, 72076, Tübingen, Germany
    Dokumententyp
    • Postprint
    Sprache
    • Englisch
    Veröffentlicht in
    • Numerische Mathematik, 2013, vol. 124, no. 3, p. 517-539. Springer-Verlag
    Andere elektronische Ausgabe
    Klassifikation
    • Informatik
    OAI-PMH-ID
    • oai:doc.rero.ch:312192
    Summary
    A method of choice for the long-time integration of constrained Hamiltonian systems is the Rattle algorithm. It is symmetric, symplectic, and nearly preserves the Hamiltonian, but it is only of order two and thus not efficient for high accuracy requirements. In this article we prove that certain symmetric linear multistep methods have the same qualitative behavior and can achieve an arbitrarily high order with a computational cost comparable to that of the Rattle algorithm