Skip to main content

Locally conservative finite difference schemes for the Modified KdV equation

Frasca-Caccia, Gianluca, Hydon, Peter E. (2019) Locally conservative finite difference schemes for the Modified KdV equation. Journal of Computational Dynamics, 6 (2). pp. 307-323. ISSN 2158-2491. E-ISSN 2158-2505. (doi:10.3934/jcd.2019015) (Access to this publication is currently restricted. You may be able to access a copy if URLs are provided) (KAR id:76694)

PDF Author's Accepted Manuscript
Language: English

Restricted to Repository staff only until 2 December 2020.
Contact us about this Publication
[img]
Official URL
http://dx.doi.org/10.3934/jcd.2019015

Abstract

Finite diffrence schemes that preserve two conservation laws of a given partial differential equation can be found directly by a recently-developed symbolic approach. Until now, this has been used only for equations with quadratic nonlinearity. In principle, a simplified version of the direct approach also works for equations with polynomial nonlinearity of higher degree. For the Modified Korteweg-de Vries equation, whose nonlinear term is cubic, this approach yields several new families of second-order accurate schemes that preserve mass and either energy or momentum. Two of these families contain Average Vector Field schemes of the type developed by Quispel and co-workers. Numerical tests show that each family includes schemes that are highly accurate compared to other mass-preserving methods that can be found in the literature.

Item Type: Article
DOI/Identification number: 10.3934/jcd.2019015
Uncontrolled keywords: Finite difference methods, conservation laws
Subjects: Q Science > QA Mathematics (inc Computing science) > QA297 Numerical analysis
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User: Peter Hydon
Date Deposited: 22 Sep 2019 16:13 UTC
Last Modified: 25 Feb 2020 13:54 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/76694 (The current URI for this page, for reference purposes)
Frasca-Caccia, Gianluca: https://orcid.org/0000-0002-4703-1424
Hydon, Peter E.: https://orcid.org/0000-0002-3732-4813
  • Depositors only (login required):

Downloads

Downloads per month over past year