Linear energy-preserving integrators for Poisson systems

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Energy-diminishing integration of gradient systems (2014, methodology): “If the constraints c(y) = 0 are linear or quadratic, condition (4.4) it equivalent to ∇c ( u(t0 + cih) )T u̇(t0 + cih) = 0 and the analysis of Cohen & Hairer (2011) can be applied to prove order 2s.”
An energy-preserving exponentially-fitted continuous stage Runge–Kutta method for Hamiltonian systems (2014, methodology): “High-order energy-preserving method for Poisson systems was constructed by Cohen–Hairer [15], where the authors extended the energy-preserving cRK method [30] to a kind of partitioned methods.”