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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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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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Periodic solution of circular Sitnikov restricted four-body problem using multiple scales method
Archive of Applied Mechanics, 2022Ashok Kumar Pal +2 more
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Multiple Scale and Singular Perturbation Methods
1996J. Kevorkian, J. D. Cole
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Forced Vibrations of Strongly Nonlinear Systems with Multiple Scales Lindstedt Poincaré Method
Mathematical and Computational Applications, 2011Mehmet Pakdemirli, H Boyaci
exaly
Modelling of Langevin Equations by the Method of Multiple Scales
IFAC-PapersOnLine, 2015Juergen Geiser
exaly