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Symmetry 2010, 2(2), 868-883; doi:10.3390/sym2020868

Lie Symmetry Preservation by Finite Difference Schemes for the Burgers Equation

LEPTIAB - Université de La Rochelle, Avenue Michel Crépeau, 17042 La Rochelle Cedex 01, France
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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)
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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 (CC BY 3.0).

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MDPI and ACS Style

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

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