A Koopman Operator Tutorial with Othogonal Polynomials
Numerical Analysis
2022-07-15 v2 Numerical Analysis
Analysis of PDEs
Abstract
The Koopman Operator (KO) offers a promising alternative methodology to solve ordinary differential equations analytically. The solution of the dynamical system is analyzed in terms of observables, which are expressed as a linear combination of the eigenfunctions of the system. Coefficients are evaluated via the Galerkin method, using Legendre polynomials as a set of orthogonal basis functions. This tutorial provides a detailed analysis of the Koopman theory, followed by a rigorous explanation of the KO implementation in a computer environment, where a line-by-line description of a MATLAB code solves the Duffing oscillator application.
Cite
@article{arxiv.2111.07485,
title = {A Koopman Operator Tutorial with Othogonal Polynomials},
author = {Simone Servadio and David Arnas and Richard Linares},
journal= {arXiv preprint arXiv:2111.07485},
year = {2022}
}
Comments
22 pages. arXiv admin note: text overlap with arXiv:2110.12119