Abstract
We consider ordinary differential equations (ODEs) with a known Lyapunov function V. To ensure that a numerical integrator reflects the correct dynamical behaviour of the system, the numerical integrator should have V as a discrete Lyapunov function. Only second-order geometric integrators of this type are known for arbitrary Lyapunov functions. In this paper we describe projection-based methods of arbitrary order that preserve any given Lyapunov function.
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