On the limit cycle of a generalized van der Pol equation
type: Item
instance of: scholarly article
title: On the limit cycle of a generalized van der Pol equation
zbMATH Open document ID: 0776.70014
DOI: 10.1016/0020-7462(93)90060-X
author: G. M. Moremedi
author: D. P. Mason
author: V. M. Gorringe
published in: International Journal of Non-Linear Mechanics
publication date: 1993-11-14T00:00:00Z
review text: The limit cycle of a generalized van der Pol equation of the form \(\ddot u+u=\varepsilon(1-u^{2n})\dot u\) is investigated, where \(\varepsilon\) is small and \(n\) is any positive integer. Using the derivative expansion version of the method of multiple scales, a perturbation solution is derived for the displacement to first order in \(\varepsilon\) and for the phase to second order in \(\varepsilon\). The perturbation solution is compared with numerical solutions obtained using the IMSL routines DIVPRK and DIVPAG. The first-order perturbation solution becomes less accurate as \(n\) increases.
Mathematics Subject Classification ID: 70K05
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 405079
zbMATH Keywords: derivative expansion version
zbMATH Keywords: method of multiple scales
zbMATH Keywords: perturbation solution
zbMATH Keywords: numerical solutions
zbMATH Keywords: DIVPRK
zbMATH Keywords: DIVPAG
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 405079