A variational complex for difference equations
type: Item
instance of: scholarly article
title: A variational complex for difference equations
zbMATH Open document ID: 1057.39013
author: Peter E. Hydon
author: E. L. Mansfield
published in: Foundations of Computational Mathematics
publication date: 2004-10-28T00:00:00Z
review text: The authors state and prove an analogue of the Poincaré lemma for exact forms on a lattice. From the results, a variational complex for difference equations is constructed and, furthermore, it is proved to be locally exact. In order to calculate the Lagrangians for discrete Euler-Lagrange systems, homotopy maps are applied. In addition, such maps lead to a systematic technique for deriving conservation laws of a given system of difference equations, even if it is not an Euler-Lagrange system.
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 14F43
Mathematics Subject Classification ID: 58A10
zbMATH DE Number: 2111602
zbMATH Keywords: difference forms
zbMATH Keywords: variational complex
zbMATH Keywords: difference equations
zbMATH Keywords: cohomology
zbMATH Keywords: Poincaré lemma
zbMATH Keywords: homotopy maps
zbMATH Keywords: Euler-Lagrange system
reviewed by: Wan-Tong Li
MaRDI profile type: Publication
full work available at URL: s10208-002-0071-9
OpenAlex ID: W2075518648
DOI: 10.1007/S10208-002-0071-9
description: scientific article; zbMATH DE number 2111602