Numerical integrators that contract volume
Numerical Analysis
2025-10-20 v1 Numerical Analysis
Dynamical Systems
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.
Cite
@article{arxiv.math/9808115,
title = {Numerical integrators that contract volume},
author = {Robert I McLachlan and G R W Quispel},
journal= {arXiv preprint arXiv:math/9808115},
year = {2025}
}
Comments
8 pages, LaTeX source