Abstract
We study the application of Runge-Kutta schemes to Hamiltonian systems of ordinary differential equations. We investigate which schemes possess the canonical property of the Hamiltonian flow. We also consider the issue of exact conservation in the time-discretization of the continuous invariants of motion.
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Sanz-Serna, J.M. Runge-kutta schemes for Hamiltonian systems. BIT 28, 877–883 (1988). https://doi.org/10.1007/BF01954907
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DOI: https://doi.org/10.1007/BF01954907