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Article

Geometric Numerical Integration of Liénard Systems via a Contact Hamiltonian Approach

1
Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, University of Groningen, 9747 AG Groningen, The Netherlands
2
Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas (IIMAS–UNAM), Mexico City 04510, Mexico
*
Author to whom correspondence should be addressed.
Academic Editor: Marian Ioan Munteanu
Mathematics 2021, 9(16), 1960; https://doi.org/10.3390/math9161960
Received: 20 July 2021 / Accepted: 10 August 2021 / Published: 16 August 2021
(This article belongs to the Special Issue Differential Geometry: Structures on Manifolds and Their Applications)
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. View Full-Text
Keywords: contact geometry; geometric integrators; Liénard systems; nonlinear oscillations contact geometry; geometric integrators; Liénard systems; nonlinear oscillations
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    Doi: 10.5281/zenodo.5115110
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MDPI and ACS Style

Zadra, F.; Bravetti, A.; Seri, M. Geometric Numerical Integration of Liénard Systems via a Contact Hamiltonian Approach. Mathematics 2021, 9, 1960. https://doi.org/10.3390/math9161960

AMA Style

Zadra F, Bravetti A, Seri M. Geometric Numerical Integration of Liénard Systems via a Contact Hamiltonian Approach. Mathematics. 2021; 9(16):1960. https://doi.org/10.3390/math9161960

Chicago/Turabian Style

Zadra, Federico, Alessandro Bravetti, and Marcello Seri. 2021. "Geometric Numerical Integration of Liénard Systems via a Contact Hamiltonian Approach" Mathematics 9, no. 16: 1960. https://doi.org/10.3390/math9161960

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