Highly Accurate Analytical Approximate Solution to a Nonlinear Pseudo-Oscillator.
A second-order Newton method is presented to construct analytical approximate solutions to a nonlinear pseudo-oscillator in which the restoring force is inversely proportional to the dependent variable. The nonlinear equation is first expressed in a specific form, and it is then solved in two steps,...
| Published in: | Zeitschrift für Naturforschung Section A: A Journal of Physical Sciences Vol. 72; no. 7; pp. 673 - 677 |
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| Main Authors: | , , |
| Format: | Article |
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De Gruyter
Jul2017
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| Subjects: | |
| Online Access: | View this record in EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=123990581&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 123990581 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 09320784 FL07 jtl: Zeitschrift für Naturforschung Section A: A Journal of Physical Sciences issn: 09320784 maglogo: N pubinfo: dt: Jul2017 vid: 72 iid: 7 pid: 1734 pub: De Gruyter artinfo: ui: 123990581 10.1515/zna-2017-0127 ppf: 673 ppct: 4 formats: tig: atl: Highly Accurate Analytical Approximate Solution to a Nonlinear Pseudo-Oscillator. aug: au: Baisheng Wu Weijia Liu Lim, C. W. affil: School of Electro-Mechanical Engineering, Guangdong University of Technology, Guangzhou 510006, P. R. China Department of Architecture and Civil Engineering, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, P. R. China su: Newton-Raphson method Iterative methods (Mathematics) Nonlinear oscillators Taylor's series Restoring force (Physics) sug: subj: Newton-Raphson method Iterative methods (Mathematics) Nonlinear oscillators Taylor's series Restoring force (Physics) keyword: Analytical Approximation Harmonic Balance Nonlinear Pseudo-Oscillator Second-Order Newton Method ab: A second-order Newton method is presented to construct analytical approximate solutions to a nonlinear pseudo-oscillator in which the restoring force is inversely proportional to the dependent variable. The nonlinear equation is first expressed in a specific form, and it is then solved in two steps, a predictor and a corrector step. In each step, the harmonic balance method is used in an appropriate manner to obtain a set of linear algebraic equations. With only one simple second-order Newton iteration step, a short, explicit, and highly accurate analytical approximate solution can be derived. The approximate solutions are valid for all amplitudes of the pseudo-oscillator. Furthermore, the method incorporates second-order Taylor expansion in a natural way, and it is of significant faster convergence rate. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y dt: @attributes: year: 2017 holdings: @attributes: islocal: N |
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