New methods for calculating the stability of periodic solutions
type: Item
instance of: scholarly article
title: New methods for calculating the stability of periodic solutions
zbMATH Open document ID: 0632.65088
DOI: 10.1016/0898-1221(87)90045-9
author: B. George
publication date: 1987-01-01T00:00:00Z
review text: The standard way to calculate the monodromy matrix M for autonomous systems of n first-order differential equations requires storage proportional to \(n^ 2\). Two new algorithms for calculating M are proposed; the first, by integrating a differential equation of order \(2n+2\), requires storage of order n. The second is applicable if the periodic solution is calculated by multiple shooting and involves nearly no work. Numerical methods are included discussing features of both algorithms.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L07
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 4028794
zbMATH Keywords: stability of periodic solutions
zbMATH Keywords: monodromy matrix
zbMATH Keywords: autonomous systems
zbMATH Keywords: multiple shooting
reviewed by: Antonio de Castro
describes a project that uses: BIFPACK
MaRDI profile type: Publication
full work available at URL: 0898-1221(87)90045-9
OpenAlex ID: W2070088588
cites work: On the Nature of the Spectrum of Singular Second Order Linear Differential Equations
cites work: Q5584086
cites work: Q3685717
cites work: Roads to turbulence in dissipative dynamical systems
cites work: Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
cites work: Q3923300
cites work: DERPER - An algorithm for the continuation of periodic solutions in ordinary differential equations
cites work: Numerical computation of periodic orbits that bifurcate from stationary solutions of ordinary differential equations
cites work: Q3930015
cites work: Q3857636
cites work: Q5659089
cites work: Klassische Runge-Kutta-Formeln fünfter und siebenter Ordnung mit Schrittweiten-Kontrolle
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 4028794