Two-sided approximation to periodic solutions of ordinary differential equations
type: Item
instance of: scholarly article
title: Two-sided approximation to periodic solutions of ordinary differential equations
zbMATH Open document ID: 0799.65077
DOI: 10.1007/BF01385704
published in: Numerische Mathematik
publication date: 1994-11-17T00:00:00Z
full work available at URL: https://eudml.org/doc/133769
review text: A two-sided approximation to the periodic orbit of an autonomous ordinary differential equation system is presented. It is proved that the implicit and explicit Euler difference methods approximate the periodic solution from inner and outer sides separately, provided the periodic orbit is convex and stable. A numerical example is given to illustrate the result and to point out that the convex condition is necessary for the difference methods in a one-sided approximation and the numerical orbit no longer possesses a one-sided approximation property, if the periodic orbit is not convex.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L12
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 569198
zbMATH Keywords: autonomous system
zbMATH Keywords: two-sided approximation
zbMATH Keywords: periodic orbit
zbMATH Keywords: Euler difference methods
zbMATH Keywords: periodic solution
zbMATH Keywords: numerical example
author: L.-Q. Zhang
reviewed by: Maria Gousidou-Koutita
MaRDI profile type: Publication
cites work: Q4744562
cites work: Q5848416
cites work: Computation of periodic solutions of nonlinear ODEs
cites work: Invariant curves for numerical methods
cites work: Q3702407
cites work: Numerical solution of bifurcation problems for ordinary differential equations
cites work: Numerical computation of periodic orbits that bifurcate from stationary solutions of ordinary differential equations
cites work: Q3990257
cites work: Asymptotic expansion and geometric properties of the spline collocation periodic solution of an ODE system
OpenAlex ID: W2050863884
description: scientific article; zbMATH DE number 569198