Geometric Numerical Integration of Liénard Systems via a Contact Hamiltonian Approach
Starting from a contact Hamiltonian description of Liénard systems, we introduce a new family of explicit geometric integrators for these nonlinear dynamical systems. Focusing on the paradigmatic example of the van der Pol oscillator, we demonstrate that these integrators are particularly stable and...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/16/1960 |
| _version_ | 1797522974006312960 |
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| author | Federico Zadra Alessandro Bravetti Marcello Seri |
| author_facet | Federico Zadra Alessandro Bravetti Marcello Seri |
| author_sort | Federico Zadra |
| collection | DOAJ |
| description | Starting from a contact Hamiltonian description of Liénard systems, we introduce a new family of explicit geometric integrators for these nonlinear dynamical systems. Focusing on the paradigmatic example of the van der Pol oscillator, we demonstrate that these integrators are particularly stable and preserve the qualitative features of the dynamics, even for relatively large values of the time step and in the stiff regime. |
| first_indexed | 2024-03-10T08:36:53Z |
| format | Article |
| id | doaj.art-38be77b9e8b84a83a664f0a513f2f778 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T08:36:53Z |
| publishDate | 2021-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-38be77b9e8b84a83a664f0a513f2f7782023-11-22T08:34:27ZengMDPI AGMathematics2227-73902021-08-01916196010.3390/math9161960Geometric Numerical Integration of Liénard Systems via a Contact Hamiltonian ApproachFederico Zadra0Alessandro Bravetti1Marcello Seri2Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, University of Groningen, 9747 AG Groningen, The NetherlandsInstituto de Investigaciones en Matemáticas Aplicadas y en Sistemas (IIMAS–UNAM), Mexico City 04510, MexicoBernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, University of Groningen, 9747 AG Groningen, The NetherlandsStarting from a contact Hamiltonian description of Liénard systems, we introduce a new family of explicit geometric integrators for these nonlinear dynamical systems. Focusing on the paradigmatic example of the van der Pol oscillator, we demonstrate that these integrators are particularly stable and preserve the qualitative features of the dynamics, even for relatively large values of the time step and in the stiff regime.https://www.mdpi.com/2227-7390/9/16/1960contact geometrygeometric integratorsLiénard systemsnonlinear oscillations |
| spellingShingle | Federico Zadra Alessandro Bravetti Marcello Seri Geometric Numerical Integration of Liénard Systems via a Contact Hamiltonian Approach Mathematics contact geometry geometric integrators Liénard systems nonlinear oscillations |
| title | Geometric Numerical Integration of Liénard Systems via a Contact Hamiltonian Approach |
| title_full | Geometric Numerical Integration of Liénard Systems via a Contact Hamiltonian Approach |
| title_fullStr | Geometric Numerical Integration of Liénard Systems via a Contact Hamiltonian Approach |
| title_full_unstemmed | Geometric Numerical Integration of Liénard Systems via a Contact Hamiltonian Approach |
| title_short | Geometric Numerical Integration of Liénard Systems via a Contact Hamiltonian Approach |
| title_sort | geometric numerical integration of lienard systems via a contact hamiltonian approach |
| topic | contact geometry geometric integrators Liénard systems nonlinear oscillations |
| url | https://www.mdpi.com/2227-7390/9/16/1960 |
| work_keys_str_mv | AT federicozadra geometricnumericalintegrationoflienardsystemsviaacontacthamiltonianapproach AT alessandrobravetti geometricnumericalintegrationoflienardsystemsviaacontacthamiltonianapproach AT marcelloseri geometricnumericalintegrationoflienardsystemsviaacontacthamiltonianapproach |