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Melnikov's method and averaging
Celestial Mechanics, 1982Consider the differential equation \(\dot x=f^ 0(x)+\epsilon f^ 1(\omega t,x;\epsilon)\), \(x\in D\subset R^ n\) where \(f^ 0\) and \(f^ 1\) are sufficiently smooth, \(f^ 1\) is \(2\pi\)-periodic in \(\omega\) t and \(\epsilon\) is a small positive parameter. Let the unperturbed system \(\dot x=f^ 0(x)\) have a hyperbolic point.
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1993
Regular perturbation methods are based on Taylor’s formula and on implicit function theorems. However, there are many problems to which Taylor’s formula cannot be applied directly, in which case perturbation methods based on multiple time or space scales can often be used, sometimes even for chaotic systems.
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Regular perturbation methods are based on Taylor’s formula and on implicit function theorems. However, there are many problems to which Taylor’s formula cannot be applied directly, in which case perturbation methods based on multiple time or space scales can often be used, sometimes even for chaotic systems.
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State-Variables-Averaging Method
1991The state-variables-averaging method [1], [2] was the first approach to result in a complete linear model of a switching power cell. It was a major contribution to the dynamic analysis of switching structures and has been adopted by other investigators (e.g., [3], [4]).
André S. Kislovski +2 more
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The Continuous Averaging Method
2009There are several problems in perturbation theory, where standard methods do not lead to satisfactory results. We mention as examples the problem of an inclusion of a diffeomorphism into a flow in the analytic set up, and the problem of quantitative description of exponentially small effects in dynamical systems. In these cases one possible approach is
Dmitry Treschev, Oleg Zubelevich
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Water rates … averaging method
Journal AWWA, 1980In approving a rate increase for a water and sewer utility, the Supreme Court of Florida held that a Public Service Commission had not departed from the essential requirements of the law in using an averaging method to reach operations and maintenance figures in calculating its rate adjustments.
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2006
The design of engineering systems and the ability to predict their performance depend on the availability of experimental data and conceptual models that can be used to describe a physical process with a required degree of accuracy. From both a scientific and a practical point of view, it is essential that the various characteristics and properties of ...
Mamoru Ishii, Takashi Hibiki
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The design of engineering systems and the ability to predict their performance depend on the availability of experimental data and conceptual models that can be used to describe a physical process with a required degree of accuracy. From both a scientific and a practical point of view, it is essential that the various characteristics and properties of ...
Mamoru Ishii, Takashi Hibiki
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1990
In this chapter we shall consider again equations containing a small parameter e. The approximation method leads generally to asymptotic series as opposed to the convergent series studied in the preceding chapter; see section 9.2 for the basic concepts and more discussion in Sanders and Verhulst (1985), chapter 2.
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In this chapter we shall consider again equations containing a small parameter e. The approximation method leads generally to asymptotic series as opposed to the convergent series studied in the preceding chapter; see section 9.2 for the basic concepts and more discussion in Sanders and Verhulst (1985), chapter 2.
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