Hydon, P.E. and Mansfield, E.L. (2004) A variational complex for difference equations. FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, 4 (2). pp. 187-217. ISSN 1615-3375.
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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).
|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:||Judith Broom|
|Date Deposited:||19 Dec 2007 18:26|
|Last Modified:||27 Jun 2012 09:30|
|Resource URI:||http://kar.kent.ac.uk/id/eprint/712 (The current URI for this page, for reference purposes)|
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