Geometric Numerical Integration of Liénard Systems via a Contact Hamiltonian Approach

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