Explicit K-symplectic methods for nonseparable non-canonical Hamiltonian systems
Beibei Zhu(朱贝贝)1, Lun Ji(纪伦)2,3, Aiqing Zhu(祝爱卿)2,3, and Yifa Tang(唐贻发)2,3,†
1 School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China; 2 LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China; 3 School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
Abstract We propose efficient numerical methods for nonseparable non-canonical Hamiltonian systems which are explicit, K-symplectic in the extended phase space with long time energy conservation properties. They are based on extending the original phase space to several copies of the phase space and imposing a mechanical restraint on the copies of the phase space. Explicit K-symplectic methods are constructed for two non-canonical Hamiltonian systems. Numerical tests show that the proposed methods exhibit good numerical performance in preserving the phase orbit and the energy of the system over long time, whereas higher order Runge-Kutta methods do not preserve these properties. Numerical tests also show that the K-symplectic methods exhibit better efficiency than that of the same order implicit symplectic, explicit and implicit symplectic methods for the original nonseparable non-canonical systems. On the other hand, the fourth order K-symplectic method is more efficient than the fourth order Yoshida's method, the optimized partitioned Runge-Kutta and Runge-Kutta-Nyström explicit K-symplectic methods for the extended phase space Hamiltonians, but less efficient than the the optimized partitioned Runge-Kutta and Runge-Kutta-Nyström extended phase space symplectic-like methods with the midpoint permutation.
Beibei Zhu(朱贝贝), Lun Ji(纪伦), Aiqing Zhu(祝爱卿), and Yifa Tang(唐贻发) Explicit K-symplectic methods for nonseparable non-canonical Hamiltonian systems 2023 Chin. Phys. B 32 020204
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