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In long-time numerical integration of Hamiltonian systems,
and especially in molecular dynamics simulation,
it is important that the energy is well conserved. For symplectic
integrators applied with sufficiently small step size, this
is guaranteed by the existence of a modified
Hamiltonian that is exactly conserved up to exponentially small
terms. This article is concerned with the simplified
Takahashi-Imada method, which is a modification
of the Störmer-Verlet method that is as easy to implement...
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