Structure Preserving Discretizations of the Liouville Equation and their Numerical Tests
The main purpose of this article is to show how symmetry structures in partial differential equations can be preserved in a discrete world and reflected in difference schemes. Three different structure preserving discretizations of the Liouville equation are presented and then used to solve specific...
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| Видавець: | Інститут математики НАН України |
|---|---|
| Дата: | 2015 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2015
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147153 |
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| Цитувати: | Structure Preserving Discretizations of the Liouville Equation and their Numerical Tests / D. Levi, L. Martina, P. Winternitz // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 42 назв. — англ. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-147153 |
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dspace |
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irk-123456789-1471532019-02-14T01:25:39Z Structure Preserving Discretizations of the Liouville Equation and their Numerical Tests Levi, D. Martina, L. Winternitz, P. The main purpose of this article is to show how symmetry structures in partial differential equations can be preserved in a discrete world and reflected in difference schemes. Three different structure preserving discretizations of the Liouville equation are presented and then used to solve specific boundary value problems. The results are compared with exact solutions satisfying the same boundary conditions. All three discretizations are on four point lattices. One preserves linearizability of the equation, another the infinite-dimensional symmetry group as higher symmetries, the third one preserves the maximal finite-dimensional subgroup of the symmetry group as point symmetries. A 9-point invariant scheme that gives a better approximation of the equation, but significantly worse numerical results for solutions is presented and discussed. 2015 Article Structure Preserving Discretizations of the Liouville Equation and their Numerical Tests / D. Levi, L. Martina, P. Winternitz // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 42 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 17B80; 22E60; 39A14; 65Mxx DOI:10.3842/SIGMA.2015.080 http://dspace.nbuv.gov.ua/handle/123456789/147153 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
The main purpose of this article is to show how symmetry structures in partial differential equations can be preserved in a discrete world and reflected in difference schemes. Three different structure preserving discretizations of the Liouville equation are presented and then used to solve specific boundary value problems. The results are compared with exact solutions satisfying the same boundary conditions. All three discretizations are on four point lattices. One preserves linearizability of the equation, another the infinite-dimensional symmetry group as higher symmetries, the third one preserves the maximal finite-dimensional subgroup of the symmetry group as point symmetries. A 9-point invariant scheme that gives a better approximation of the equation, but significantly worse numerical results for solutions is presented and discussed. |
| format |
Article |
| author |
Levi, D. Martina, L. Winternitz, P. |
| spellingShingle |
Levi, D. Martina, L. Winternitz, P. Structure Preserving Discretizations of the Liouville Equation and their Numerical Tests Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Levi, D. Martina, L. Winternitz, P. |
| author_sort |
Levi, D. |
| title |
Structure Preserving Discretizations of the Liouville Equation and their Numerical Tests |
| title_short |
Structure Preserving Discretizations of the Liouville Equation and their Numerical Tests |
| title_full |
Structure Preserving Discretizations of the Liouville Equation and their Numerical Tests |
| title_fullStr |
Structure Preserving Discretizations of the Liouville Equation and their Numerical Tests |
| title_full_unstemmed |
Structure Preserving Discretizations of the Liouville Equation and their Numerical Tests |
| title_sort |
structure preserving discretizations of the liouville equation and their numerical tests |
| publisher |
Інститут математики НАН України |
| publishDate |
2015 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147153 |
| citation_txt |
Structure Preserving Discretizations of the Liouville Equation and their Numerical Tests / D. Levi, L. Martina, P. Winternitz // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 42 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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AT levid structurepreservingdiscretizationsoftheliouvilleequationandtheirnumericaltests AT martinal structurepreservingdiscretizationsoftheliouvilleequationandtheirnumericaltests AT winternitzp structurepreservingdiscretizationsoftheliouvilleequationandtheirnumericaltests |
| first_indexed |
2023-05-20T17:26:43Z |
| last_indexed |
2023-05-20T17:26:43Z |
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1796153311189008384 |