Improved N-th order averaging theory for periodic systems
type: Item
instance of: scholarly article
title: Improved N-th order averaging theory for periodic systems
zbMATH Open document ID: 0704.34067
DOI: 10.1016/0022-0396(90)90083-2
author: James A. Ellison
author: A. W. Sáenz
author: H. Scott Dumas
published in: Journal of Differential Equations
publication date: 1990-01-01T00:00:00Z
review text: The solution x(t;\(\epsilon\)) of a nonlinear periodic system of ordinary differential equations \(\dot x=f(t,x;\epsilon)\), \(x(0;\epsilon)=\xi\), where \(\epsilon\) is a small parameter, is approximated by an N-th order averaging procedure. Under weak smoothness assumptions on the function f(x,t;\(\epsilon\)) the asymptotic solution \(w_ N(t;\epsilon)\) is shown to be \(\epsilon^ N\)-close to the exact solution x(t;\(\epsilon\)) on a time-interval [0,T/\(\epsilon\) ]. The results are very useful for precise investigations of periodic perturbations.
Mathematics Subject Classification ID: 34E10
Mathematics Subject Classification ID: 34A12
Mathematics Subject Classification ID: 34C11
Mathematics Subject Classification ID: 34C29
zbMATH DE Number: 4154927
zbMATH Keywords: small parameter
zbMATH Keywords: averaging procedure
zbMATH Keywords: periodic perturbations
MaRDI profile type: Publication
full work available at URL: 0022-0396(90)90083-2
OpenAlex ID: W2064431160
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description: scientific article; zbMATH DE number 4154927