D. I. McLaren

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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. Mathematics Subject Classification. 65P10, 65L06. Received May 21, 2008. Published online July 8, 2009. All Runge-Kutta (RK) methods preserve arbitrary linear invariants [12],(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 dissipative structure, also preserves the correct monotonic decrease of energy. The method is illustrated by many examples. In the Hamiltonian(More)
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