ISOSYRK methods on Zeitlin’s Euler–Zeitlin system admit n-independent exponentially small modified-Hamiltonian errors for times exp(c/ε) when h = ε ℏ_n.
Fine structures inside the PreLie operad revisited
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abstract
We prove a conjecture of Chapoton from 2010 stating that the pre-Lie operad, as a Lie algebra in the symmetric monoidal category of linear species, is freely generated by the free operad on the species of cyclic Lie elements.
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Backward error analysis for matrix discretizations of 2-D Euler equations
ISOSYRK methods on Zeitlin’s Euler–Zeitlin system admit n-independent exponentially small modified-Hamiltonian errors for times exp(c/ε) when h = ε ℏ_n.