Abstract
In this paper, following the idea of constructing the mixed symplectic integrator (MSI) for a separable Hamiltonian system, we give a low order mixed symplectic integrator for an inseparable, but nearly integrable, Hamiltonian system, Although the difference schemes of the integrators are implicit, they not only have a small truncation error but, due to near integrability, also a faster convergence rate of iterative solution than ordinary implicit integrators, Moreover, these second order integrators are time-reversible.
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Liao, X. Symplectic integrator for general near-integrable Hamiltonian system. Celestial Mech Dyn Astr 66, 243–253 (1996). https://doi.org/10.1007/BF00049381
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DOI: https://doi.org/10.1007/BF00049381