Symplectic methods for non-canonical Hamiltonian systems
Symplectic Geometry
2015-10-14 v2
Abstract
We show that, when applied to any non-canonical Hamiltonian system, any integrator that is symplectic for canonical Hamiltonian problems is actually conjugate symplectic for the non-canonical structure. This result is useful because it implies that canonically symplectic methods may be successfully applied to long-time integrations of non-canonical Hamiltonian problems, thus avoiding the need to construct ad hoc new methods. Numerical results for three non-canonical Hamiltonian systems demonstrate that (canonically) symplectic methods have significant advantages in numerical accuracy and near energy preservation over non-symplectic methods.
Cite
@article{arxiv.1509.03811,
title = {Symplectic methods for non-canonical Hamiltonian systems},
author = {Beibei Zhu and Ruili Zhang and Yifa Tang and Xiongbiao Tu},
journal= {arXiv preprint arXiv:1509.03811},
year = {2015}
}
Comments
This paper has been withdrawn by the author due to a error in the theorem