A variational complex for difference equations

Hydon, Peter E., Mansfield, Elizabeth L. (2004) A variational complex for difference equations. Foundations of Computational Mathematics, 4 (2). pp. 187-217. ISSN 1615-3375. (doi:10.1007/s10208-002-0071-9) (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) (KAR id:712)

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.
Official URL: https://doi.org/DOI not available

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
DOI/Identification number:	10.1007/s10208-002-0071-9
Uncontrolled keywords:	DIRECT CONSTRUCTION METHOD; CONSERVATION-LAWS; GEOMETRIC INTEGRATION; LIE SYMMETRIES; DISCRETE; CLASSIFICATION; OPERATORS; SYSTEMS; PDES
Subjects:	Q Science > QA Mathematics (inc Computing science)
Institutional Unit:	Schools > School of Engineering, Mathematics and Physics > Mathematical Sciences
Former Institutional Unit:	Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User:	Elizabeth Mansfield
Date Deposited:	19 Dec 2007 18:26 UTC
Last Modified:	20 May 2025 11:29 UTC
Resource URI:	https://kar.kent.ac.uk/id/eprint/712 (The current URI for this page, for reference purposes)

University of Kent Author Information

Mansfield, Elizabeth L..

Creator's ORCID:	https://orcid.org/0000-0002-6778-2241
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