Equilibria, periodic orbits and computing them
Abstract
In this short exposition, we describe equilibria and periodic orbits in terms of the flow map, {\Phi}, and discuss the essentials of the Jacobian-free Newton-Krylov (JFNK) method that can be used to find them. This method requires little more than calls to an existing time stepping code, which {\Phi} can be considered to represent. Fortran90 / MATLAB code is available to try it out for yourself, where, in the template/example the method is applied to the Lorenz system. This code is problem-independent and can be applied to large systems, having initially been developed to find periodic orbits in simulations of pipe flow.
Keywords
Cite
@article{arxiv.1908.06730,
title = {Equilibria, periodic orbits and computing them},
author = {Ashley P. Willis},
journal= {arXiv preprint arXiv:1908.06730},
year = {2019}
}
Comments
EPSRC Summer School on Modal decompositions in fluid mechanics. DAMTP, Cambridge, 5-8 August 2019. 16 pages. (v2: references added, hyperlinks corrected)