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2011
The origins of the method of multiple scales go back to Krylov and Bogolyubov in 1932. The general principle behind the method is that the dependent variable is uniformly expanded in terms of two or more independent variables, nominally referred to as scales.
Vasile Marinca, Nicolae Herisanu
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The origins of the method of multiple scales go back to Krylov and Bogolyubov in 1932. The general principle behind the method is that the dependent variable is uniformly expanded in terms of two or more independent variables, nominally referred to as scales.
Vasile Marinca, Nicolae Herisanu
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A Method of Multiple Scales for Integral Equations
Journal of the Physical Society of Japan, 1981A new method is proposed for the purpose of analysing the system of weakly nonlinear integral equations. The essence of this method consists in expanding the integral operator in powers of e : \(\int _{0}^{t} \text{d}t= \sum _{n=0}^{N} \varepsilon ^{n} \text{I}_{n} + O(\varepsilon ^{N+1}),i\) where N is a positive integer, e is a small parameter ...
Yoshinori Inoue, Keiji Michihiro
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2003
In the method of matched asymptotic expansions (Chapter 5), the solution is constructed in different regions that are then patched together to form a composite expansion. The method of multiple scales1, on the other hand, starts with a generalized version of a composite expansion. This involves separate coordinates for each region, which are considered
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In the method of matched asymptotic expansions (Chapter 5), the solution is constructed in different regions that are then patched together to form a composite expansion. The method of multiple scales1, on the other hand, starts with a generalized version of a composite expansion. This involves separate coordinates for each region, which are considered
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A Perturbation Method Based on Integrating Vectors and Multiple Scales
SIAM Journal on Applied Mathematics, 1999Summary: 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 ...
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Method of multiple scales and identification of nonlinear structuraldynamic systems
24th Structures, Structural Dynamics and Materials Conference, 1983A procedure is developed to identify the parameters of a nonlinear structural dynamic system with a single degree of freedom. A cubic nonlinearity is assumed for purposes of illustration. In comparison to the direct identification procedures, which depend on either the availability of data on all four variables, namely, velocity, acceleration ...
Hanagud, S. V. +2 more
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Method of multiple scales in quantum optics
Physics Reports, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Wavelet and multiple scale reproducing kernel methods
International Journal for Numerical Methods in Fluids, 1995AbstractMultiple scale methods based on reproducing kernel and wavelet analysis are developed. These permit the response of a system to be separated into different scales. These scales can be either the wave numbers corresponding to spatial variables or the frequencies corresponding to temporal variables, and each scale response can be examined ...
Liu, Wing Kam, Chen, Yijung
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Nonlinear Optimal Control Problems and the Method of Multiple Scales
IMA Journal of Mathematical Control and Information, 1989Summary: The method of multiple scales is used to obtain an approximate solution to the problem of the optimal control of a second-order differential equation containing a small nonlinearity. Applications are made to the Duffing and van der Pol equations.
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Multiple scaling method for the calculation of threaded assemblies
Computer Methods in Applied Mechanics and Engineering, 1993Abstract The numerical computation of threaded structures usually leads to very large finite elements problems. We propose here a new method mixing FE small problems and a unidimensional elliptic problem to drastically reduce the computing costs.
Andrieux, S., Leger, A.
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The Multiple Scales Method, Homoclinic Bifurcation and Melnikov's Method for Autonomous Systems
International Journal of Bifurcation and Chaos, 1998Melnikov's method is a well-established technique for detecting homoclinic bifurcation of perturbed autonomous or forced systems. This method uses a regular perturbation expansion in terms of a small parameter in the system. Whilst the approach correctly estimates the parameter values for the bifurcation and transverse intersections of separatrices ...
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