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We show that while Runge-Kutta methods cannot preserve polynomial invariants in general , they can preserve polynomials that are the energy invariant of canonical Hamiltonian systems. All Runge-Kutta (RK) methods preserve arbitrary linear invariants [12], and some (the symplectic) RK methods preserve arbitrary quadratic invariants [4]. However, no RK method(More)
We give a systematic method for discretizing Hamiltonian partial differential equations (PDEs) with constant symplectic structure, while preserving their energy exactly. The same method, applied to PDEs with constant dissipa-tive structure, also preserves the correct monotonic decrease of energy. The method is illustrated by many examples. In the(More)
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