2015/09/13 by Beibei Zhu, Zhu, Beibei, Ruili Zhang +5
Engineering · Mathematics · Physics and Astronomy · #37M15 #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #G.5.3 #Nonlinear Waves and Solitons #Numerical methods for differential equations #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.1509.03811
openalex publication_date 2015/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.