A generalized KBM method for strongly nonlinear oscillators with slowly varying parameters
type: Item
instance of: scholarly article
title: A generalized KBM method for strongly nonlinear oscillators with slowly varying parameters
zbMATH Open document ID: 1147.34345
author: Jianping Cai
published in: Mathematical \& Computational Applications
publication date: 2008-11-17T00:00:00Z
review text: Summary: A generalized Krylov-Bogoliubov-Mitropolsky (KBM) method is extended for the study of strongly nonlinear oscillators with slowly varying parameters. The asymptotic amplitude and phase are derived and then the asymptotic solutions of arbitrary order are obtained theoretically. Cubic nonlinear oscillators with polynomial damping are studied in detail. Three examples are considered: a generalized Van der Pol oscillator, a Rayleigh equation and a pendulum with variable length. Comparisons are also made with numerical solutions to show the efficiency and accuracy of the present method.
Mathematics Subject Classification ID: 34E05
Mathematics Subject Classification ID: 34C15
Mathematics Subject Classification ID: 34E13
zbMATH DE Number: 5366541
MaRDI profile type: Publication
full work available at URL: mca12010021
OpenAlex ID: W2415422539
DOI: 10.3390/MCA12010021
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description: scientific article; zbMATH DE number 5366541