Year: 2019
Type: preprint
Abstract: In this short exposition, we describe equilibria and periodic orbits in terms of the flow map, Φ, 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 Φ 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.
Source: arXiv (Cornell University)
Author: Willis, Ashley P.
Institution: University of Sheffield
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G7323135170
OpenAlex ID: W2969060739