A Koopman Operator Tutorial with Othogonal Polynomials

Autor:	Servadio, Simone, Arnas, David, Linares, Richard
Rok vydání:	2021
Předmět:	Mathematics - Numerical Analysis Mathematics - Analysis of PDEs
Druh dokumentu:	Working Paper
Popis:	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. Comment: 22 pages. arXiv admin note: text overlap with arXiv:2110.12119
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2111.07485 Zobrazit plný text záznamu View this record from Arxiv