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

TL;DR

This paper introduces explicit K-symplectic numerical methods for nonseparable non-canonical Hamiltonian systems, extending phase space to improve long-term energy conservation and outperform traditional methods.

Contribution

The paper develops a novel class of explicit K-symplectic methods for nonseparable non-canonical Hamiltonian systems using phase space extension and mechanical restraints.

Findings

Methods outperform higher order Runge-Kutta in energy preservation

Explicit methods effectively preserve phase orbit over long time

Applicable to three non-canonical Hamiltonian systems

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 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.