Explicit K-symplectic methods for nonseparable non-canonical Hamiltonian systems  

作　　者：朱贝贝 纪伦 祝爱卿 唐贻发 Beibei Zhu;Lun Ji;Aiqing Zhu;Yifa Tang(School of Mathematics and Physics,University of Science and Technology Beijing,Beijing 100083,China;LSEC,ICMSEC,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China;School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China)

机构地区：[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

出　　处：《Chinese Physics B》2023年第2期60-79,共20页中国物理B（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant Nos. 11901564 and 12171466)。

摘　　要：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–Nystr ¨om explicit K-symplectic methods for the extended phase space Hamiltonians, but less efficient than the the optimized partitioned Runge–Kutta and Runge–Kutta–Nystr ¨om extended phase space symplectic-like methods with the midpoint permutation.

关 键 词：non-canonical Hamiltonian systems NONSEPARABLE explicit K-symplectic methods splitting method 

分 类 号：O241[理学—计算数学]