English

An explicit pseudo-energy conserving time-integration scheme for Hamiltonian dynamics

Numerical Analysis 2020-08-14 v1 Numerical Analysis

Abstract

We propose a new explicit pseudo-energy and momentum conserving scheme for the time integration of Hamiltonian systems. The scheme, which is formally second-order accurate, is based on two key ideas: the integration during the time-steps of forces between free-flight particles and the use of momentum jumps at the discrete time nodes leading to a two-step formulation for the acceleration. The pseudo-energy conservation is established under exact force integration, whereas it is valid to second-order accuracy in the presence of quadrature errors. Moreover, we devise an asynchronous version of the scheme that can be used in the framework of slow-fast time-stepping strategies. The scheme is validated against classical benchmarks and on nonlinear or inhomogeneous wave propagation problems.

Keywords

Cite

@article{arxiv.2008.06000,
  title  = {An explicit pseudo-energy conserving time-integration scheme for Hamiltonian dynamics},
  author = {Frédéric Marazzato and Alexandre Ern and Christian Mariotti and Laurent Monasse},
  journal= {arXiv preprint arXiv:2008.06000},
  year   = {2020}
}
R2 v1 2026-06-23T17:50:29.720Z