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    Error Estimation of Fourier Series Expansion and Implication to Solution Accuracy for Nonlinear Dynamical Systems

    Source: Journal of Computational and Nonlinear Dynamics:;2017:;volume( 012 ):;issue: 001::page 11002
    Author:
    Chen, Y. M.
    ,
    Lv, Z. R.
    ,
    Liu, J. K.
    DOI: 10.1115/1.4034127
    Publisher: 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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      Error Estimation of Fourier Series Expansion and Implication to Solution Accuracy for Nonlinear Dynamical Systems

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    contributor authorChen, Y. M.
    contributor authorLv, Z. R.
    contributor authorLiu, J. K.
    date accessioned2017-11-25T07:20:17Z
    date available2017-11-25T07:20:17Z
    date copyright2016/1/9
    date issued2017
    identifier issn1555-1415
    identifier othercnd_012_01_011002.pdf
    identifier urihttp://138.201.223.254:8080/yetl1/handle/yetl/4236342
    description abstractFourier 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.
    publisherThe American Society of Mechanical Engineers (ASME)
    titleError Estimation of Fourier Series Expansion and Implication to Solution Accuracy for Nonlinear Dynamical Systems
    typeJournal Paper
    journal volume12
    journal issue1
    journal titleJournal of Computational and Nonlinear Dynamics
    identifier doi10.1115/1.4034127
    journal fristpage11002
    journal lastpage011002-6
    treeJournal of Computational and Nonlinear Dynamics:;2017:;volume( 012 ):;issue: 001
    contenttypeFulltext
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    DSpace software copyright © 2002-2015  DuraSpace
    نرم افزار کتابخانه دیجیتال "دی اسپیس" فارسی شده توسط یابش برای کتابخانه های ایرانی | تماس با یابش
    yabeshDSpacePersian