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Numerical integrators that contract volume

Robert I McLachlan·G R W Quispel
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Abstract

We study numerical integrators that contract phase space volume even when the ODE does so at an arbitrarily small rate. This is done by a splitting into two-dimensional contractive systems. We prove a sufficient condition for Runge-Kutta methods to have the appropriate contraction property for these two-dimensional systems; the midpoint rule is an example.

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Robert I McLachlan, G R W Quispel. 1998-08-27. Numerical integrators that contract volume. https://arxiv.org/abs/math/9808115

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