Runge-Kutta and Networks
Numerical Analysis
2019-09-02 v1 Numerical Analysis
Category Theory
Abstract
We categorify the RK family of numerical integration methods (explicit and implicit). Namely we prove that if a pair of ODEs are related by an affine map then the corresponding discrete time dynamical systems are also related by the map. We show that in practice this works well when the pairs of related ODEs come from the coupled cell networks formalism and, more generally, from fibrations of networks of manifolds.
Cite
@article{arxiv.1908.11453,
title = {Runge-Kutta and Networks},
author = {Lee DeVille and Eugene Lerman and James Schmidt},
journal= {arXiv preprint arXiv:1908.11453},
year = {2019}
}
Comments
11 pages, comments welcome