Title

Dispersive properties of multisymplectic integrators

Authors

Authors

C. M. Schober;T. H. Wlodarczyk

Comments

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Abbreviated Journal Title

J. Comput. Phys.

Keywords

multisymplectic methods; box schemes; leapfrog method; dispersion; relation; sine-gordon equation; double-pole soliton; WAVE ACTION; CONSERVATION; SCHEMES; PDES; EQUATION; Computer Science, Interdisciplinary Applications; Physics, Mathematical

Abstract

Multisymplectic (MS) integrators, i.e. numerical schemes which exactly preserve a discrete space-time symplectic structure, are a new class of structure preserving algorithms for solving Hamiltonian PDEs. In this paper we examine the dispersive properties of MS integrators for the linear wave and sine-Gordon equations. In particular a leapfrog in space and time scheme (a member of the Lobatto Runge-Kutta family of methods) and the Preissman box scheme are considered. We find the numerical dispersion relations are monotonic and that the sign of the group velocity is preserved. The group velocity dispersion (GVD) is found to provide significant information and succinctly explain the qualitative differences in the numerical solutions obtained with the different schemes. Further, the numerical dispersion relations for the linearized sine-Gordon equation provides information on the ability of the NIS integrators to capture the sine-Gordon dynamics. We are able to link the numerical dispersion relations to the total energy of the various methods, thus providing information on the coarse grid behavior of NIS integrators in the nonlinear regime. (C) 2008 Elsevier Inc. All rights reserved.

Journal Title

Journal of Computational Physics

Volume

227

Issue/Number

10

Publication Date

1-1-2008

Document Type

Article

Language

English

First Page

5090

Last Page

5104

WOS Identifier

WOS:000255447000015

ISSN

0021-9991

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