Skip to content
University of Maryland LibrariesDigital Repository at the University of Maryland
    • Login
    View Item 
    •   DRUM
    • A. James Clark School of Engineering
    • Institute for Systems Research Technical Reports
    • View Item
    •   DRUM
    • A. James Clark School of Engineering
    • Institute for Systems Research Technical Reports
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Almost Symplectic Runge-Kutta Schemes for Hamiltonian Systems

    Thumbnail
    View/Open
    TR_2004-1.pdf (1.273Mb)
    No. of downloads: 846

    Date
    2004
    Author
    Tan, Xiaobo
    Metadata
    Show full item record
    Abstract
    Symplectic Runge-Kutta schemes for the integration of general Hamiltonian systems are implicit. In practice one has to solve the implicit algebraic equations using some iterative approximation method, in which case the resulting integration scheme is no longer symplectic. In this paper we first analyze the preservation of the symplectic structure under two popular approximation schemes, fixed-point iteration and Newton's method, respectively. Error bounds for the symplectic structure are established when N fixed-point iterations or N iterations of Newton's method are used. The implications of these results for the implementation of symplectic methods are discussed and then explored through extensive numerical examples. Numerical comparisons with non-symplectic Runge-Kutta methods and pseudo-symplectic methods are also presented.
    URI
    http://hdl.handle.net/1903/6408
    Collections
    • Institute for Systems Research Technical Reports

    DRUM is brought to you by the University of Maryland Libraries
    University of Maryland, College Park, MD 20742-7011 (301)314-1328.
    Please send us your comments.
    Web Accessibility
     

     

    Browse

    All of DRUMCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

    My Account

    LoginRegister
    Pages
    About DRUMAbout Download Statistics

    DRUM is brought to you by the University of Maryland Libraries
    University of Maryland, College Park, MD 20742-7011 (301)314-1328.
    Please send us your comments.
    Web Accessibility