Conservation properties of multisymplectic integrators

    Authors

    A. L. Islas;C. M. Schober

    Comments

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    Abbreviated Journal Title

    Futur. Gener. Comp. Syst.

    Keywords

    multisymplectic integrators; Hamiltonian PDEs; conservation laws; long-time dynamics; HAMILTONIAN PDES; DISCRETIZATIONS; EQUATIONS; BEHAVIOR; Computer Science, Theory & Methods

    Abstract

    Recent results on the local and global properties of multisymplectic discretizations of Hamiltonian PDEs are discussed. We consider multisymplectic (MS) schemes based on Fourier spectral approximations and show that, in addition to a MS conservation law, conservation laws related to linear symmetries of the PDE are preserved exactly. We compare spectral integrators (MS versus non-symplectic) for the nonlinear Schrodinger (NLS) equation, focusing on their ability to preserve local conservation laws and global invariants, over long times. Using Lax-type nonlinear spectral diagnostics we find that the MS spectral method provides an improved resolution of complicated phase space structures. (c) 2004 Elsevier B.V. All rights reserved.

    Journal Title

    Future Generation Computer Systems-the International Journal of Grid Computing Theory Methods and Applications

    Volume

    22

    Issue/Number

    4

    Publication Date

    1-1-2006

    Document Type

    Article; Proceedings Paper

    Language

    English

    First Page

    412

    Last Page

    422

    WOS Identifier

    WOS:000234904100006

    ISSN

    0167-739X

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