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An Alternative Example of the Method of Multiple Scales
SIAM Review, 2000Summary: An alternative example of the method of multiple scales is presented. This example arises in the study of the classical heat equation with a slowly varying flux imposed at one end. The module presents introductory ideas about dimensionless variables, multiple-scale expansions, and scaling of the dependent variable.
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The Sitnikov Problem Investigation with the Method of Multiple Scales
Iranian Journal of Science and Technology, Transactions A: Science, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Manshadi, Ali Dehghan +1 more
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Multiple scale finite element methods
International Journal for Numerical Methods in Engineering, 1991AbstractNew temporal and spatial discretization methods are developed for multiple scale structural dynamic problems. The concept of fast and slow time scales is introduced for the temporal discretization. The required time step is shown to be dependent only on the slow time scale, and therefore, large time steps can be used for high frequency problems.
Liu, Wing Kam +2 more
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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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1999
Abstract In this chapter we apply the multiple-scale method to the study of problem (6.1). The method is presented in Section 7.1 and a formal asymptotic expansion for u ε is obtained. The goal of Section 7.2 is to prove the error estimate stated in Theorem 6.3.
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Abstract In this chapter we apply the multiple-scale method to the study of problem (6.1). The method is presented in Section 7.1 and a formal asymptotic expansion for u ε is obtained. The goal of Section 7.2 is to prove the error estimate stated in Theorem 6.3.
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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 wavelet-based edge detection method by scale multiplication
Object recognition supported by user interaction for service robots, 2003A wavelet-based multiscale edge detection scheme is presented in this paper. By multiplying the wavelet coefficients at two adjacent scales to magnify significant structures and suppress noise, we determined edges as the local maxima directly in the scale product after an efficient thresholding, instead of first forming the edge maps at several scales ...
Lei Zhang 0006, Paul Bao
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Method of Multiple Fault Isolation in Large Scale Systems
IEEE Transactions on Control Systems Technology, 2012In this paper, problems of the online diagnostics of multiple faults in large scale systems are presented. Possibilities of recognition of multiple faults based on the knowledge of signatures of the single faults are discussed. The distinction between simultaneous faults and the series of faults is introduced and defined.
Jan Maciej Kóscielny +2 more
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