Title

Backward error analysis for multisymplectic discretizations of Hamiltonian PDEs

Authors

Authors

A. L. Islas;C. M. Schober

Comments

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

Abbreviated Journal Title

Math. Comput. Simul.

Keywords

multisymplectic schemes; Hamiltonian PDEs; backward error analysis; SYMPLECTIC INTEGRATION METHODS; EQUATIONS; Computer Science, Interdisciplinary Applications; Computer Science, ; Software Engineering; Mathematics, Applied

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 Schrodinger 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. (c) 2005 IMACS. Published by Elsevier B.V. All rights reserved.

Journal Title

Mathematics and Computers in Simulation

Volume

69

Issue/Number

3-4

Publication Date

1-1-2005

Document Type

Article; Proceedings Paper

Language

English

First Page

290

Last Page

303

WOS Identifier

WOS:000230029600008

ISSN

0378-4754

Share

COinS