Fast Galerkin method and its application to determine periodic solutions of nonlinear oscillators
type: Item
instance of: scholarly article
title: Fast Galerkin method and its application to determine periodic solutions of nonlinear oscillators
zbMATH Open document ID: 0606.73025
DOI: 10.1016/0020-7462(87)90012-6
author: B. George
published in: International Journal of Non-Linear Mechanics
publication date: 1987-01-01T00:00:00Z
review text: The Galerkin method is an approximate method which finds wide application in solving differential and integral equations. But a large amount of computation is needed in order to get a high order approximation by using the method. Applying the FFT technique to form a so-called fast Galerkin method we can reduce the computation work greatly, when taking trigonometric functions as characteristic functions. Taking the periodic solution of nonlinear oscillators as an example, we illustrate the procedure and the efficiency of the method. Moreover, with some modifications we extend the applicability of the method, so that not only periodic solutions with known periods, but also those with unknown periods, as well as subharmonics, combination tones, etc., can be treated with the method. Some techniques are described which can be used to simplify the computation.
Mathematics Subject Classification ID: 74H45
Mathematics Subject Classification ID: 70K99
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65T40
zbMATH DE Number: 3980604
zbMATH Keywords: FFT technique
zbMATH Keywords: fast Galerkin method
zbMATH Keywords: trigonometric functions as characteristic functions
zbMATH Keywords: periodic solution of nonlinear oscillators
zbMATH Keywords: known periods
zbMATH Keywords: unknown periods
zbMATH Keywords: subharmonics
zbMATH Keywords: combination tones
MaRDI profile type: Publication
full work available at URL: 0020-7462(87)90012-6
OpenAlex ID: W2017585699
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description: scientific article; zbMATH DE number 3980604