Results 251 to 260 of about 15,981,515 (305)

A Perturbation Method Based on Integrating Vectors and Multiple Scales

SIAM Journal on Applied Mathematics, 1999
Summary: A new perturbation method based on integrating vectors and multiple scales is presented for regularly perturbed systems of ordinary differential equations. Asymptotic approximations to first integrals are constructed on long time-scales, that is, on time-scales of order \(\varepsilon^{-n}\), where \(\varepsilon\) is a small parameter and \(n ...
Wim van Horssen
openaire   +3 more sources

Resolving Controversies in the Application of the Method of Multiple Scales and the Generalized Method of Averaging

Nonlinear Dynamics, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +3 more sources

Comparing the direct normal form method with harmonic balance and the method of multiple scales [PDF]

open access: yesProcedia Engineering, 2017
Approximate analytical methods have been used extensively for finding approximate solutions to nonlinear ordinary differential equations. In this paper we compare the recently developed direct normal form transformation with two other very well known and
S A Neild, D J Wagg
exaly   +2 more sources

Solitons in Superlattices: Multiple Scales Method

International Journal of Theoretical Physics, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tian, Qiang, Zhang, Qiyi, Zhou, Hui
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Multiple Scale Method

2021
In multiple scale method, the independent variable will be replaced by several variables, each with a scaled down speed of variation. Replacing the independent variable, makes a nonlinear ordinary differential equation to be transformed to a series of linear partial differential equations. Combination of the solutions of the linear partial differential
openaire   +1 more source

A HIGHER ORDER METHOD OF MULTIPLE SCALES

Journal of Sound and Vibration, 1997
Summary: Perturbation methods are often applied in the analysis of weakly nonlinear dynamic systems. The method of multiple scales, for instance, is a common choice. \textit{Z. Rahman} and \textit{T. D. Burton} [ibid. 133, No. 3, 369--379 (1989; Zbl 1235.70099)] proposed a version of the method of multiple scales which can be used to determine the ...
Lee, C. L., Lee, C.-T.
openaire   +1 more source

On the Reconstitution Problem in the Multiple Time-Scale Method

Nonlinear Dynamics, 1999
The authors consider general systems of the form \(\ddot q+F(q, \dot q,t;\mu)=0\), where \(\mu\) is a vector containing small physical quantities, or small deviations from the critical values of other parameters. A perturbation parameter \(\varepsilon\) is introduced by the equation \(\mu= \varepsilon \widehat\mu\), \(\widehat\mu= O(1)\), then the ...
LUONGO, Angelo, Paolone A.
openaire   +4 more sources

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