Title

Backward Error Analysis For Multisymplectic Discretizations Of Hamiltonian Pdes

Keywords

Backward error analysis; Hamiltonian PDEs; Multisymplectic schemes

Abstract

Several recently developed multisymplectic schemes for Hamiltonian PDEs have been shown to preserve associated local conservation laws and constraints very well in long time numerical simulations. Backward error analysis for PDEs, or the method of modified equations, is a useful technique for studying the qualitative behavior of a discretization and provides insight into the preservation properties of the scheme. In this paper we initiate a backward error analysis for PDE discretizations, in particular of multisymplectic box schemes for the nonlinear Schrödinger equation. We show that the associated modified differential equations are also multisymplectic and derive the modified conservation laws which are satisfied to higher order by the numerical solution. Higher order preservation of the modified local conservation laws is verified numerically. © 2005 IMACS. Published by Elsevier B.V. All rights reserved.

Publication Date

6-24-2005

Publication Title

Mathematics and Computers in Simulation

Volume

69

Issue

3-4

Number of Pages

290-303

Document Type

Article; Proceedings Paper

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.matcom.2005.01.006

Socpus ID

19044372348 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/19044372348

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