  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.
