Abstract
It is well-known that if a symplectic integrator is applied to a Hamiltonian system, then the modified equation, whose solutions interpolate the numerical solutions, is again Hamiltonian. We investigate this property from the variational side. We present a technique to construct a Lagrangian for the modified equation from the discrete Lagrangian of a variational integrator.
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This research is funded by the DFG Collaborative Research Center TRR 109 “Discretization in Geometry and Dynamics”. The author would like to thank Yuri Suris for inspiring discussions and for his critical feedback on the early versions of this manuscript.
