Based on a known observation that symplecticity is preserved under certain Sundman time transformations, adaptive symplectic integrators of an arbitrary order are constructed for separable Hamiltonian systems, for two classes of scaling functions. Due to symplecticity, these adaptive integrators have excellent long-time energy behaviour, which is theoretically explained using standard results on the existence of a modified Hamiltonian function.
In Contrast to reversible adaptive integration, the constructed methods have good long-time behaviour also for non-reversible systems. Numerical examples of this are given.
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