  Efficient fourth order symplectic integrators are proposed for numerical
integration of separable Hamiltonian systems H(p,q)=T(p)+V(q). Symmetric
splitting coefficients with five to nine stages are obtained by higher order
decomposition of the simple harmonic oscillator. The performance of the methods
is evaluated for various Hamiltonian systems: Integration errors are compared
to those of acclaimed integrators composed by S. Blanes et al. (2013), W. Kahan
et al. (1999) and H. Yoshida (1990). Numerical tests indicate that the
integrators obtained in this paper perform significantly better than previous
integrators for common Hamiltonian systems.
