A variational complex for difference equations

Hydon, Peter E. and Mansfield, Elizabeth L. (2004) A variational complex for difference equations. Foundations of Computational Mathematics, 4 (2). pp. 187-217. ISSN 1615-3375. (doi:DOI not available) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

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Abstract

An analogue of the Poincare lemma for exact forms on a lattice is stated and proved. Using this result as a starting-point, a variational complex for difference equations is constructed and is proved to be locally exact. The proof uses homotopy maps, which enable one to calculate Lagrangians for discrete Euter-Lagrange systems. Furthermore, such maps lead to a systematic technique for deriving conservation laws of a given system of difference equations (whether or not it is an Euler-Lagrange system).

Item Type: Article
Uncontrolled keywords: DIRECT CONSTRUCTION METHOD; CONSERVATION-LAWS; GEOMETRIC INTEGRATION; LIE SYMMETRIES; DISCRETE; CLASSIFICATION; OPERATORS; SYSTEMS; PDES
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science
Depositing User: Elizabeth L Mansfield
Date Deposited: 19 Dec 2007 18:26
Last Modified: 15 Jan 2016 15:36
Resource URI: https://kar.kent.ac.uk/id/eprint/712 (The current URI for this page, for reference purposes)
ORCiD (Mansfield, Elizabeth L.): http://orcid.org/0000-0002-6778-2241
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