Title

Dispersion, Group Velocity, And Multisymplectic Discretizations

Keywords

Box schemes; Dispersion relation; Leap-frog method; Sine-Gordon equation

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. © 2009 IMACS.

Publication Date

12-1-2009

Publication Title

Mathematics and Computers in Simulation

Volume

80

Issue

4

Number of Pages

741-751

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.matcom.2009.08.015

Socpus ID

70649099137 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/70649099137

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