Dispersion, group velocity, and multisymplectic discretizations

C.M. Schober and T.H. Wlodarczyk

Mathematics and Computers in Simulation (MATCOM), 2009, vol. 80, issue 4, 741-751

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.

Keywords: Box schemes; Leap-frog method; Dispersion relation; Sine-Gordon equation (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:80:y:2009:i:4:p:741-751

DOI: 10.1016/j.matcom.2009.08.015

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