Numerical solution of nonlinear equation to combined deterministic and narrow-band random excitation
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Publication Details
Author list: Chinviriyasit W., Chinviriyasit S.
Publisher: World Scientific Publishing
Publication year: 2008
Journal: International Journal of Modern Physics B: Condensed Matter Physics; Statistical Physics; Atomic, Molecular and Optical Physics (0217-9792)
Volume number: 22
Issue number: 21
Start page: 3655
End page: 3675
Number of pages: 21
ISSN: 0217-9792
eISSN: 1793-6578
Languages: English-Great Britain (EN-GB)
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Abstract
The Duffing oscillator to combined deterministic and narrow-band random excitation, which is a nonlinear equation, is studied and solved numerically using three numerical methods based on finite difference schemes. Method 1, the well-known Euler method, is an explicit method; Method 2 is an implicit first-order method which does not bring contrived chaos into the solution; and Method 3 is based on two first-order methods which is second-order method and is chaos-free. In a series of numerical experiments, it is seen that the proposed methods have superior stability properties to those of the well-known Euler and fourth-order Runge-Kutta methods to which they are compared. When extended to the numerical solution of Duffing oscillator to combined deterministic and narrow-band random excitation, the developed methods give the correct steady-state solutions compared with the literature. ฉ 2008 World Scientific Publishing Company.
Keywords
Duffing oscillator, Implicit method, second-order method, Narrow-band random
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