NDLI: Numerical Solutions of Duffing Equations Involving Linear Integral with Shifted Chebyshev Polynomials

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Numerical Solutions of Duffing Equations Involving Linear Integral with Shifted Chebyshev Polynomials

Content Provider	Semantic Scholar
Author	Anapalı, Ayşe Öztürk, Yalçın Gülsu, Mustafa
Copyright Year	2015
Abstract	The purpose of this study is to give a shifted Chebyshev polynomial approximation for the solution of Duffing-van der Pol equation involving linear integral term (DEILI). For this purpose, a new Chebyshev collocation method is introduced. This method is based on taking the truncated shifted Chebyshev expansion of the function. This method based on first taking the truncated Chebyshev series of the solution function in the DEILI and then, transforms DEILI and given conditions into a matrix equation and then, we have the system of nonlinear algebraic equation using collocation points. Then, solving the system of algebraic equations we have the coefficients of the truncated Chebyshev series. In addition, examples that illustrate the pertinent features of the method are presented, and the results of study are discussed. 1.Introduction Duffing equation is a mathematical model to describe a classical oscillator in a double-well by a periodical driven, which has been widely investigated in chaotic phenomena (Mickens, 1981; Guckenheimer and Holmes, 1983). It arises in a variety of different scientific fields such as periodic orbit extraction, non-uniformity caused by an infinite domain, nonlinear mechanical oscillators, prediction of
File Format	PDF HTM / HTML
Alternate Webpage(s)	http://fenbildergi.aku.edu.tr/1502/021301(1-11).pdf
Language	English
Access Restriction	Open
Subject Keyword	Algebraic equation Approximation Chebyshev polynomials Circuit complexity Coefficient Collocation method Linear algebra Mathematical model Mathematics Nonlinear system Numerical method Oscillator Device Component Periodicals Polynomial Relevance Van der Pol oscillator
Content Type	Text
Resource Type	Article

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