Title

Dispersion, group velocity, and multisymplectic discretizations

Authors

Authors

C. M. Schober;T. H. Wlodarczyk

Comments

Authors: contact us about adding a copy of your work at STARS@ucf.edu

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

Share

COinS