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Geometric Numerical Integration of Liénard Systems via a Contact Hamiltonian Approach

Author

Listed:
  • 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)

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.

Suggested Citation

  • Federico Zadra & Alessandro Bravetti & Marcello Seri, 2021. "Geometric Numerical Integration of Liénard Systems via a Contact Hamiltonian Approach," Mathematics, MDPI, vol. 9(16), pages 1-26, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1960-:d:615521
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    Cited by:

    1. Marian Ioan Munteanu, 2022. "Preface to: Differential Geometry: Structures on Manifolds and Their Applications," Mathematics, MDPI, vol. 10(13), pages 1-3, June.

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