Numerical calculation of the frequency of an oscillatory problem
type: Item
instance of: scholarly article
title: Numerical calculation of the frequency of an oscillatory problem
zbMATH Open document ID: 0974.65071
DOI: 10.1016/S0893-9659(99)00170-6
author: Yanyan Li
published in: Applied Mathematics Letters
publication date: 2001-07-15T00:00:00Z
review text: In recent times, a number of special numerical methods has been proposed for the integration of oscillatory problems of the form \(x''+\omega^2x=\varepsilon f(x,x')\). These methods depend on the frequency of the oscillation. A rough approximation is given by \(\omega\). The authors show how it can easily be improved using the first approximation of Krylov and Bogolyubov. In three numerical experiments with a code developed by the authors, it is shown that the numerical results become much better, if the improved approximation for the frequency is used. The examples include the Duffing oscillator, two coupled anharmonic oscillators and a satellite problem in focal variables.
reviewed by: Werner M. Seiler
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34C10
zbMATH DE Number: 1428511
zbMATH Keywords: oscillatory problem
zbMATH Keywords: frequency determination
zbMATH Keywords: Krylov-Bogolyubov method
zbMATH Keywords: numerical experiments
zbMATH Keywords: Duffing oscillator
zbMATH Keywords: anharmonic oscillators
zbMATH Keywords: satellite problem
MaRDI profile type: Publication
cites work: Nonlinear differential equations and dynamical systems
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cites work: Q3682833
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full work available at URL: s0893-9659(99)00170-6
OpenAlex ID: W2020504384
description: scientific article; zbMATH DE number 1428511