Three sixth-order explicit symplectic Runge–Kutta-Nystrom methods with exact parameters

For separable Hamiltonian systems, we construct first ever three symplectic explicit Runge–Kutta-Nyström methods of six orders with exact parameters. We numerically and theoretically compare these three new exact methods with the only existing exact 6-th order symplectic explicit partitioned Runge–Kutta method and two approximate 6-th order symplectic explicit Runge–Kutta-Nyström methods. These new methods are more accurate and stable.