Geometric Numerical Integration of Liénard Systems via a Contact Hamiltonian Approach

Federico Zadra, Alessandro Bravetti and Marcello Seri
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Federico Zadra: Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, University of Groningen, 9747 AG Groningen, The Netherlands
Alessandro Bravetti: Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas (IIMAS–UNAM), Mexico City 04510, Mexico
Marcello Seri: Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, University of Groningen, 9747 AG Groningen, The Netherlands

Mathematics, 2021, vol. 9, issue 16, 1-26

Abstract: 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.

Keywords: contact geometry; geometric integrators; Liénard systems; nonlinear oscillations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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