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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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Multiple scales methods in meteorology
2010With emphasis on meteorological applications, we discuss here the fluid dynamical fundamental governing equations, their nondimensionalization including the identification of key nondimensional parameters, and a general approach to meteorological modelling based on multiple scales asymptotics.
Klein, Rupert +3 more
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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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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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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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THE KBM DERIVATIVE EXPANSION METHOD IS EQUIVALENT TO THE MULTIPLE-TIME-SCALES METHOD
Journal of Sound and Vibration, 1997Summary: Several perturbation methods are commonly used to predict the free and forced response of weakly non-linear oscillators. The Krylov-Bogoliubov-Mitropolsky (KBM) and multiple-time-scales (MTS) methods use expansions of dependent variables, ordinary time derivatives, and some system parameters to convert the equations of motion into a set of ...
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Nonlinear Dynamics, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The Method of Multiple Scales and the ∈-Power Series
1998The perturbation strategy known as the “method of multiple scales” lies at the heart of solitary wave theory. First, it is the vehicle by which three-dimensional reality is approximated by one-dimensional models such as the Korteweg-deVries equation. One might call this “reduction of dimension”.
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