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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Bibliographic Details
Published in:Symmetry (Basel) 2010-06, Vol.2 (2), p.868-883
Main Authors: Chhay, Marx, Hamdouni, Aziz
Format: Article
Language:English
Subjects:
finite differences scheme
invariant scheme
Lie symmetry
moving frames
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Summary: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.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym2020868