Lie Symmetry Preservation by Finite Difference Schemes for the Burgers Equation

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 algor...

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Main Authors:	Marx Chhay, Aziz Hamdouni
Format:	Article
Language:	English
Published:	MDPI AG 2010-04-01
Series:	Symmetry
Subjects:	invariant scheme Lie symmetry moving frames finite differences scheme
Online Access:	http://www.mdpi.com/2073-8994/2/2/868/

id	doaj-99914ef40f47416186fa9d8ace0e88e4
record_format	Article
spelling	doaj-99914ef40f47416186fa9d8ace0e88e42020-11-24T23:12:48ZengMDPI AGSymmetry2073-89942010-04-012286888310.3390/sym2020868Lie Symmetry Preservation by Finite Difference Schemes for the Burgers EquationMarx ChhayAziz HamdouniInvariant 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. http://www.mdpi.com/2073-8994/2/2/868/invariant schemeLie symmetrymoving framesfinite differences scheme
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Marx Chhay Aziz Hamdouni
spellingShingle	Marx Chhay Aziz Hamdouni Lie Symmetry Preservation by Finite Difference Schemes for the Burgers Equation Symmetry invariant scheme Lie symmetry moving frames finite differences scheme
author_facet	Marx Chhay Aziz Hamdouni
author_sort	Marx Chhay
title	Lie Symmetry Preservation by Finite Difference Schemes for the Burgers Equation
title_short	Lie Symmetry Preservation by Finite Difference Schemes for the Burgers Equation
title_full	Lie Symmetry Preservation by Finite Difference Schemes for the Burgers Equation
title_fullStr	Lie Symmetry Preservation by Finite Difference Schemes for the Burgers Equation
title_full_unstemmed	Lie Symmetry Preservation by Finite Difference Schemes for the Burgers Equation
title_sort	lie symmetry preservation by finite difference schemes for the burgers equation
publisher	MDPI AG
series	Symmetry
issn	2073-8994
publishDate	2010-04-01
description	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.
topic	invariant scheme Lie symmetry moving frames finite differences scheme
url	http://www.mdpi.com/2073-8994/2/2/868/
work_keys_str_mv	AT marxchhay liesymmetrypreservationbyfinitedifferenceschemesfortheburgersequation AT azizhamdouni liesymmetrypreservationbyfinitedifferenceschemesfortheburgersequation
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Lie Symmetry Preservation by Finite Difference Schemes for the Burgers Equation

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