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.

References in corpus (16)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Contact Hamiltonian Mechanics
• Contact Hamiltonian Systems
• Explicit methods in extended phase space for inseparable Hamiltonian problems
• Geometry of Thermodynamic Processes
• New contributions to the Hamiltonian and Lagrangian contact formalisms for dissipative mechanical systems and their symmetries
• Contact manifolds and dissipation, classical and quantum
• A contact geometry framework for field theories with dissipation
• Singular Lagrangians and precontact Hamiltonian Systems
• Contact variational integrators
• A thermostat algorithm generating target ensembles
• Conservative perturbation theory for nonconservative systems
• On the geometry of discrete contact mechanics
• Numerical integration in celestial mechanics: a case for contact geometry
• High order analysis of the limit cycle of the van der Pol oscillator
• Structure-preserving numerical integrators for Hodgkin-Huxley-type systems