Chebyshev spectral methods for computing center manifolds
type: Item
instance of: scholarly article
title: Chebyshev spectral methods for computing center manifolds
zbMATH Open document ID: 1481.37099
author: Takeshi Saito
author: Kazuyuki Yagasaki
published in: Journal of Computational Dynamics
publication date: 2021-08-02T00:00:00Z
review text: Computing the stable, unstable and center manifolds of a given dynamical system gives one much insight into the properties and evolution of the system. For this reason, several techniques for their determination (both analytical and numerical) have been proposed over the years. In the particular case of center manifolds, numerical techniques based on Taylor polynomials provide reasonable approximations, but only in a neighborhood of an equilibrium point or a periodic orbit. The aim of the present paper consists in approximating the center manifold by certain functions obeying a system of partial differential equations. These functions are subsequently determined by applying Chebyshev spectral methods. As a result, the validity of the approximations is extended to larger regions in the phase space. The technique is described in detail and illustrated for several dynamical systems, both Hamiltonian and non-Hamiltonian, with one-, two- and four-dimensional center manifolds. Although the technique shows accurate results for the examples considered, computing higher-dimensional center manifolds still presents challenging computational issues.
reviewed by: Fernando Casas
Mathematics Subject Classification ID: 37M21
Mathematics Subject Classification ID: 37M15
Mathematics Subject Classification ID: 65P10
zbMATH DE Number: 7377231
zbMATH Keywords: center manifold
zbMATH Keywords: dynamical system
zbMATH Keywords: numerical computation
zbMATH Keywords: Chebyshev spectral method
describes a project that uses: Mathematica
describes a project that uses: AUTO-07P
describes a project that uses: AUTO
describes a project that uses: Differentiation Matrix Suite
describes a project that uses: Matlab
MaRDI profile type: Publication
full work available at URL: jcd.2021008
OpenAlex ID: W3139239751
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DOI: 10.3934/JCD.2021008
description: scientific article; zbMATH DE number 7377231