On the two-scale method for the problem of perturbed one-frequency oscillations
type: Item
instance of: scholarly article
title: On the two-scale method for the problem of perturbed one-frequency oscillations
zbMATH Open document ID: 0963.34040
DOI: 10.1007/BF02557325
author: A. M. Il'in
published in: Theoretical and Mathematical Physics
publication date: 2001-06-11T00:00:00Z
review text: The author considers asymptotical properties of the solution to ordinary differential equations with a small parameter \({{d\rho} \over {d \varphi}} =\varepsilon G(\rho, \varphi , \varepsilon)\). Under some general asumptions, the two-scale method is used to construct an asymptotic expansion of the solution up to any order in \(\varepsilon\) on a time interval \(t=O(\varepsilon^{-1})\).
reviewed by: S. Yanchuk
Mathematics Subject Classification ID: 34E13
Mathematics Subject Classification ID: 34C15
Mathematics Subject Classification ID: 34A45
Mathematics Subject Classification ID: 70K60
Mathematics Subject Classification ID: 34D05
Mathematics Subject Classification ID: 34E05
zbMATH DE Number: 1465884
zbMATH Keywords: two-scale method
zbMATH Keywords: perturbed oscillations
zbMATH Keywords: asymptotic methods
MaRDI profile type: Publication
cites work: Q5682682
cites work: On a solution of the van der Pol equation
cites work: Q5848416
full work available at URL: https://doi.org/10.1007/bf02557325
OpenAlex ID: W2002277436
description: scientific article; zbMATH DE number 1465884