Abstract
We show that the theorems of Sanz-Serna and Eirola and Sanz-Serna concerning the symplecticity of Runge-Kutta and Linear Multistep methods, respectively, follow from the fact that these methods preserve quadratic integral invariants and are closed under differentiation and restriction to closed subsystems.
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Bochev, P.B., Scovel, C. On quadratic invariants and symplectic structure. BIT 34, 337–345 (1994). https://doi.org/10.1007/BF01935643
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DOI: https://doi.org/10.1007/BF01935643