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Efficient fourth order symplectic integrators are proposed for numericalintegration of separable Hamiltonian systems H(p,q)=T(p)+V(q). Symmetricsplitting coefficients with five to nine stages are obtained by higher orderdecomposition of the simple harmonic oscillator. The performance of the methodsis evaluated for various Hamiltonian systems: Integration errors are comparedto those of acclaimed integrators composed by S. Blanes et al. (2013), W. Kahanet al. (1999) and H. Yoshida (1990). Numerical tests indicate that theintegrators obtained in this paper perform significantly better than previousintegrators for common Hamiltonian systems.

Efficient fourth order symplectic integrators for near-harmonic separable Hamiltonian systems