Dispersion, group velocity, and multisymplectic discretizations

    Authors

    C. M. Schober;T. H. Wlodarczyk

    Comments

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    Abbreviated Journal Title

    Math. Comput. Simul.

    Keywords

    Box schemes; Leap-frog method; Dispersion relation; Sine-Gordon equation; INTEGRATORS; SCHEMES; EQUATION; PDES; Computer Science, Interdisciplinary Applications; Computer Science, ; Software Engineering; Mathematics, Applied

    Abstract

    This paper examines the dispersive properties of multisymplectic discretizations of linear and nonlinear PDEs. We focus on a leapfrog in space and time scheme and the Preissman box scheme. We find that the numerical dispersion relations are monotonic and determine the relationship between the group velocities of the different numerical schemes. The group velocity dispersion is used to explain the qualitative differences in the numerical solutions obtained with the different schemes. Furthermore. the numerical dispersion relation is found to be relevant when determining the ability of the discretizations to resolve nonlinear dynamics. (C) 2009 IMACS. Published by Elsevier B.V. All rights reserved.

    Journal Title

    Mathematics and Computers in Simulation

    Volume

    80

    Issue/Number

    4

    Publication Date

    1-1-2009

    Document Type

    Article; Proceedings Paper

    Language

    English

    First Page

    741

    Last Page

    751

    WOS Identifier

    WOS:000273183600011

    ISSN

    0378-4754

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