Error Estimation of Fourier Series Expansion and Implication to Solution Accuracy for Nonlinear Dynamical SystemsSource: Journal of Computational and Nonlinear Dynamics:;2017:;volume( 012 ):;issue: 001::page 11002DOI: 10.1115/1.4034127Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: Fourier series expansion (FSE) plays a pivotal role in frequency domain analysis of a wide variety of nonlinear dynamical systems. To the best of our knowledge, there are two general approaches for FSE, i.e., a collocation method (CM) previously proposed by the authors and the classical discrete FSE. Though there are huge applications of these methods, it still remains much less understood in their relationship and error estimation. In this study, we proved that they are equivalent if time points are uniformly chosen. Based on this property, more importantly, the error was analytically estimated for both discrete Fourier expansion (DFE) and CM. Furthermore, we revealed that the accuracy of frequency domain solutions cannot be improved by increasing the number of time points alone, whereas it absolutely depends upon the truncated number of harmonics. It indicates that an appropriate number of time points should be chosen in FSE if frequency domain solutions are targeted for nonlinear dynamical systems, especially those with complicated functions.
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contributor author | Chen, Y. M. | |
contributor author | Lv, Z. R. | |
contributor author | Liu, J. K. | |
date accessioned | 2017-11-25T07:20:17Z | |
date available | 2017-11-25T07:20:17Z | |
date copyright | 2016/1/9 | |
date issued | 2017 | |
identifier issn | 1555-1415 | |
identifier other | cnd_012_01_011002.pdf | |
identifier uri | http://138.201.223.254:8080/yetl1/handle/yetl/4236342 | |
description abstract | Fourier series expansion (FSE) plays a pivotal role in frequency domain analysis of a wide variety of nonlinear dynamical systems. To the best of our knowledge, there are two general approaches for FSE, i.e., a collocation method (CM) previously proposed by the authors and the classical discrete FSE. Though there are huge applications of these methods, it still remains much less understood in their relationship and error estimation. In this study, we proved that they are equivalent if time points are uniformly chosen. Based on this property, more importantly, the error was analytically estimated for both discrete Fourier expansion (DFE) and CM. Furthermore, we revealed that the accuracy of frequency domain solutions cannot be improved by increasing the number of time points alone, whereas it absolutely depends upon the truncated number of harmonics. It indicates that an appropriate number of time points should be chosen in FSE if frequency domain solutions are targeted for nonlinear dynamical systems, especially those with complicated functions. | |
publisher | The American Society of Mechanical Engineers (ASME) | |
title | Error Estimation of Fourier Series Expansion and Implication to Solution Accuracy for Nonlinear Dynamical Systems | |
type | Journal Paper | |
journal volume | 12 | |
journal issue | 1 | |
journal title | Journal of Computational and Nonlinear Dynamics | |
identifier doi | 10.1115/1.4034127 | |
journal fristpage | 11002 | |
journal lastpage | 011002-6 | |
tree | Journal of Computational and Nonlinear Dynamics:;2017:;volume( 012 ):;issue: 001 | |
contenttype | Fulltext |