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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2010-04-01
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| Series: | Symmetry |
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| Online Access: | http://www.mdpi.com/2073-8994/2/2/868/ |
| _version_ | 1811184846119108608 |
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| author | Marx Chhay Aziz Hamdouni |
| author_facet | Marx Chhay Aziz Hamdouni |
| author_sort | Marx Chhay |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-04-11T13:20:25Z |
| format | Article |
| id | doaj.art-99914ef40f47416186fa9d8ace0e88e4 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-11T13:20:25Z |
| publishDate | 2010-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-99914ef40f47416186fa9d8ace0e88e42022-12-22T04:22:15ZengMDPI 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 |
| 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 |
| title | 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_short | Lie Symmetry Preservation by Finite Difference Schemes for the Burgers Equation |
| title_sort | lie symmetry preservation by finite difference schemes for the burgers equation |
| 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 |