An Example of Uniform Approximation near a Caustic
نویسندگان
چکیده
منابع مشابه
Anomalous Reeections near a Caustic
Waves propagating in a medium with highly variable refractive index tend to focus forming caustics. The energy content of the waveeeld in the vicinity of a caustic is higher than that of the ambient eld away from the caustic. Consequently, waves scattering from heterogeneities located near caustics have more energy than a eld scattering a little further away from the caustic. For a suitable cho...
متن کاملWave Propagation near a Smooth Caustic
A caustic is an envelope of a family of rays of geometrical optics. At a caustic, the usual equations of geometrical optics are not valid. We give a formal asymptotic series, valid both near and away from a smooth caustic, which satisfies the differential equation exactly. In the case of high-frequency oscillations, the solution is represented in terms of the Airy function and its derivative. T...
متن کاملA uniform approximation method to solve absolute value equation
In this paper, we propose a parametric uniform approximation method to solve NP-hard absolute value equations. For this, we uniformly approximate absolute value in such a way that the nonsmooth absolute value equation can be formulated as a smooth nonlinear equation. By solving the parametric smooth nonlinear equation using Newton method, for a decreasing sequence of parameters, we can get the ...
متن کاملPWL approximation of dynamical systems: an example
The piecewise-linear approximation technique developed by Julián et al. in the past few years is applied to dynamical systems dependent on given numbers of state variables and parameters. Referring to a particular example, i.e., the two-dimensional Bautin equation, it is shown that an accurately approximated dynamical system preserves both the dynamical (trajectories) and the structural-stabili...
متن کاملA method to obtain the best uniform polynomial approximation for the family of rational function
In this article, by using Chebyshev’s polynomials and Chebyshev’s expansion, we obtain the best uniform polynomial approximation out of P2n to a class of rational functions of the form (ax2+c)-1 on any non symmetric interval [d,e]. Using the obtained approximation, we provide the best uniform polynomial approximation to a class of rational functions of the form (ax2+bx+c)-1 for both cases b2-4a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Journal of the Acoustical Society of America
سال: 1974
ISSN: 0001-4966
DOI: 10.1121/1.3437972