Backward error analysis for multisymplectic discretizations of Hamiltonian PDEs

    Authors

    A. L. Islas;C. M. Schober

    Comments

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    Abbreviated Journal Title

    Math. Comput. Simul.

    Keywords

    multisymplectic schemes; Hamiltonian PDEs; backward error analysis; SYMPLECTIC INTEGRATION METHODS; EQUATIONS; Computer Science, Interdisciplinary Applications; Computer Science, ; Software Engineering; Mathematics, Applied

    Abstract

    Several recently developed multisymplectic schemes for Hamiltonian PDEs have been shown to preserve associated local conservation laws and constraints very well in long time numerical simulations. Backward error analysis for PDEs, or the method of modified equations, is a useful technique for studying the qualitative behavior of a discretization and provides insight into the preservation properties of the scheme. In this paper we initiate a backward error analysis for PDE discretizations, in particular of multisymplectic box schemes for the nonlinear Schrodinger equation. We show that the associated modified differential equations are also multisymplectic and derive the modified conservation laws which are satisfied to higher order by the numerical solution. Higher order preservation of the modified local conservation laws is verified numerically. (c) 2005 IMACS. Published by Elsevier B.V. All rights reserved.

    Journal Title

    Mathematics and Computers in Simulation

    Volume

    69

    Issue/Number

    3-4

    Publication Date

    1-1-2005

    Document Type

    Article; Proceedings Paper

    Language

    English

    First Page

    290

    Last Page

    303

    WOS Identifier

    WOS:000230029600008

    ISSN

    0378-4754

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