Next Article in Journal
Symmetry versus Asymmetry in the Molecules of Life: Homomeric Protein Assemblies
Next Article in Special Issue
Magnetization Dynamics Symmetry in Spin Torque Induced Magnetization Switching
Previous Article in Journal / Special Issue
The Symmetry Group of the Non-Isothermal Navier–Stokes Equations and Turbulence Modelling
Symmetry 2010, 2(2), 868-883; doi:10.3390/sym2020868
Article

Lie Symmetry Preservation by Finite Difference Schemes for the Burgers Equation

*  and
LEPTIAB - Université de La Rochelle, Avenue Michel Crépeau, 17042 La Rochelle Cedex 01, France
* Author to whom correspondence should be addressed.
Received: 21 December 2009 / Revised: 30 March 2010 / Accepted: 15 April 2010 / Published: 19 April 2010
(This article belongs to the Special Issue Feature Papers: Symmetry Concepts and Applications)
Download PDF [308 KB, uploaded 19 April 2010]

Abstract

Invariant numerical schemes possess properties that may overcome the numerical properties of most of classical schemes. When they are constructed with moving frames, invariant schemes can present more stability and accuracy. The cornerstone is to select relevant moving frames. We present a new algorithmic process to do this. The construction of invariant schemes consists in parametrizing the scheme with constant coefficients. These coefficients are determined in order to satisfy a fixed order of accuracy and an equivariance condition. Numerical applications with the Burgers equation illustrate the high performances of the process.
Keywords: invariant scheme; Lie symmetry; moving frames; finite differences scheme invariant scheme; Lie symmetry; moving frames; finite differences scheme
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Share & Cite This Article

Further Mendeley | CiteULike
Export to BibTeX |
EndNote
MDPI and ACS Style

Chhay, M.; Hamdouni, A. Lie Symmetry Preservation by Finite Difference Schemes for the Burgers Equation. Symmetry 2010, 2, 868-883.

View more citation formats

Related Articles

Article Metrics

For more information on the journal, click here

Comments

Cited By

[Return to top]
Symmetry EISSN 2073-8994 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert