$Numerical solution of a class of space fractional nonlinear vibration equations with periodic boundary conditions by the Fourier spectral method$
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Numerical solution of a class of space fractional nonlinear vibration equations with periodic boundary conditions by the Fourier spectral method

Nonlinear vibration arises everywhere in engineering. So far there is no method to track the exact trajectory of a space fractional nonlinear oscillator; therefore, a sophisticated numerical method is much needed to elucidate its basic properties. For this purpose, a numerical method that combines t...

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Autores principales:	Zhixin Zhu, Che Han, Haitao Liu, Li Cao, Wang Yulan
Formato:	article
Lenguaje:	EN
Publicado:	SAGE Publishing 2021
Materias:	Control engineering systems. Automatic machinery (General) TJ212-225 Acoustics. Sound QC221-246
Acceso en línea:	https://doaj.org/article/4258b359489744d3ac23a8c03aa5e90e
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spelling	oai:doaj.org-article:4258b359489744d3ac23a8c03aa5e90e2021-12-02T01:35:03ZNumerical solution of a class of space fractional nonlinear vibration equations with periodic boundary conditions by the Fourier spectral method1461-34842048-404610.1177/14613484211038781https://doaj.org/article/4258b359489744d3ac23a8c03aa5e90e2021-12-01T00:00:00Zhttps://doi.org/10.1177/14613484211038781https://doaj.org/toc/1461-3484https://doaj.org/toc/2048-4046Nonlinear vibration arises everywhere in engineering. So far there is no method to track the exact trajectory of a space fractional nonlinear oscillator; therefore, a sophisticated numerical method is much needed to elucidate its basic properties. For this purpose, a numerical method that combines the Fourier spectral method with the Runge–Kutta method is proposed. Its accuracy and efficiency have been demonstrated numerically. This approach has full physical understanding and numerical access; thus, it can be used to solve many types of nonlinear space fractional partial differential equations with periodic boundary conditions.Zhixin ZhuChe HanHaitao LiuLi CaoWang YulanSAGE PublishingarticleControl engineering systems. Automatic machinery (General)TJ212-225Acoustics. SoundQC221-246ENJournal of Low Frequency Noise, Vibration and Active Control, Vol 40 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Control engineering systems. Automatic machinery (General) TJ212-225 Acoustics. Sound QC221-246
spellingShingle	Control engineering systems. Automatic machinery (General) TJ212-225 Acoustics. Sound QC221-246 Zhixin Zhu Che Han Haitao Liu Li Cao Wang Yulan Numerical solution of a class of space fractional nonlinear vibration equations with periodic boundary conditions by the Fourier spectral method
description	Nonlinear vibration arises everywhere in engineering. So far there is no method to track the exact trajectory of a space fractional nonlinear oscillator; therefore, a sophisticated numerical method is much needed to elucidate its basic properties. For this purpose, a numerical method that combines the Fourier spectral method with the Runge–Kutta method is proposed. Its accuracy and efficiency have been demonstrated numerically. This approach has full physical understanding and numerical access; thus, it can be used to solve many types of nonlinear space fractional partial differential equations with periodic boundary conditions.
format	article
author	Zhixin Zhu Che Han Haitao Liu Li Cao Wang Yulan
author_facet	Zhixin Zhu Che Han Haitao Liu Li Cao Wang Yulan
author_sort	Zhixin Zhu
title	Numerical solution of a class of space fractional nonlinear vibration equations with periodic boundary conditions by the Fourier spectral method
title_short	Numerical solution of a class of space fractional nonlinear vibration equations with periodic boundary conditions by the Fourier spectral method
title_full	Numerical solution of a class of space fractional nonlinear vibration equations with periodic boundary conditions by the Fourier spectral method
title_fullStr	Numerical solution of a class of space fractional nonlinear vibration equations with periodic boundary conditions by the Fourier spectral method
title_full_unstemmed	Numerical solution of a class of space fractional nonlinear vibration equations with periodic boundary conditions by the Fourier spectral method
title_sort	numerical solution of a class of space fractional nonlinear vibration equations with periodic boundary conditions by the fourier spectral method
publisher	SAGE Publishing
publishDate	2021
url	https://doaj.org/article/4258b359489744d3ac23a8c03aa5e90e
work_keys_str_mv	AT zhixinzhu numericalsolutionofaclassofspacefractionalnonlinearvibrationequationswithperiodicboundaryconditionsbythefourierspectralmethod AT chehan numericalsolutionofaclassofspacefractionalnonlinearvibrationequationswithperiodicboundaryconditionsbythefourierspectralmethod AT haitaoliu numericalsolutionofaclassofspacefractionalnonlinearvibrationequationswithperiodicboundaryconditionsbythefourierspectralmethod AT licao numericalsolutionofaclassofspacefractionalnonlinearvibrationequationswithperiodicboundaryconditionsbythefourierspectralmethod AT wangyulan numericalsolutionofaclassofspacefractionalnonlinearvibrationequationswithperiodicboundaryconditionsbythefourierspectralmethod
_version_	1718402953456386048

Numerical solution of a class of space fractional nonlinear vibration equations with periodic boundary conditions by the Fourier spectral method

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