Geometric numerical integration of Lìenard systems via a contact Hamiltonian approach

05/08/2020

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by   Federico Zadra, et al.

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Starting from a contact Hamiltonian description of Lìenard 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.