Grant, Timothy J., Hydon, Peter E. (2013) Characteristics of Conservation Laws for Difference Equations. Foundations of Computational Mathematics, 13 (4). pp. 667692. ISSN 16153375. EISSN 16153383. (doi:10.1007/s1020801391512) (KAR id:52906)
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Official URL http://dx.doi.org/10.1007/s1020801391512 
Abstract
Each conservation law of a given partial differential equation is determined (up to equivalence) by a function known as the characteristic. This function is used to find conservation laws, to prove equivalence between conservation laws, and to prove the converse of Noether's Theorem. Transferring these results to difference equations is nontrivial, largely because difference operators are not derivations and do not obey the chain rule for derivatives. We show how these problems may be resolved and illustrate various uses of the characteristic. In particular, we establish the converse of Noether's Theorem for difference equations, we show (without taking a continuum limit) that the conservation laws in the infinite family generated by Rasin and Schiff are distinct, and we obtain all fivepoint conservation laws for the potential LotkaVolterra equation.
Item Type:  Article 

DOI/Identification number:  10.1007/s1020801391512 
Uncontrolled keywords:  Conservation laws; Difference equations; Noether's Theorem; 
Subjects: 
Q Science > QA Mathematics (inc Computing science) > QA297 Numerical analysis Q Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations Q Science > QC Physics > QC20 Mathematical Physics 
Divisions:  Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science 
Depositing User:  Peter Hydon 
Date Deposited:  06 Jan 2016 09:39 UTC 
Last Modified:  16 Feb 2021 13:31 UTC 
Resource URI:  https://kar.kent.ac.uk/id/eprint/52906 (The current URI for this page, for reference purposes) 
Hydon, Peter E.:  https://orcid.org/0000000237324813 
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