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 three non-canonical Hamiltonian systems. Numerical results show that they outperform the higher order Runge-Kutta methods in preserving the phase orbit and the energy of the system over long time.

翻译：我们为不可分离的非卡门性汉密尔顿系统提出了高效的数字方法,这些方法很明确,在长的阶段空间中具有长时期节能特性的K-显性,其基础是将最初的阶段空间扩大到几个阶段空间的复制件,对阶段空间的复制件施加机械限制,为三种非卡门性汉密尔顿系统建造了明显的K-显性方法,数字结果表明,这些方法在保护阶段轨道和系统能源方面比较高的龙格-库塔方法长一段时间。