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arXiv · 1509.03811

Symplectic methods for non-canonical Hamiltonian systems

Beibei Zhu·Ruili Zhang·Yifa Tang·Xiongbiao Tu
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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.

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Beibei Zhu, Ruili Zhang, Yifa Tang, Xiongbiao Tu. 2015-09-13. Symplectic methods for non-canonical Hamiltonian systems. https://arxiv.org/abs/1509.03811

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