On surface radiation conditions for an ellipse
نویسندگان
چکیده
منابع مشابه
On surface radiation conditions for an ellipse
We compare several On Surface Radiation Boundary Conditions in two dimensions, for solving the Helmholtz equation exterior to an ellipse. We also introduce a new boundary condition for an ellipse based on amodal expansion inMathieu functions. We compare the OSRC to a finite difference method. © 2009 Elsevier B.V. All rights reserved.
متن کاملOn The Perimeter of an Ellipse
Let E be the ellipse with major and minor radii a and b respectively, and Pbe its perimeter, then P = lim 4 tan(p/n)(a + b + 2) Σ a2 cos2 (2k-2)Pi/n+ sin2 (2k-2)Pi/n; where n = 2m. So without considering the limit, it gives a reasonable approxi-mation for P, it means that we can choose n large enough such that the amountof error be less than any given small number. On the other hand, the form...
متن کاملOn the Perimeter of an Ellipse
Computing accurate approximations to the perimeter of an ellipse is a favourite problem of mathematicians, attracting luminaries such as Ramanujan [1, 2, 3]. As is well known, the perimeter, , of an ellipse with semimajor axis a and semiminor axis b can be expressed exactly as a complete elliptic integral of the second kind, which can also be written as a Gaussian hypergeometric function, (1) ...
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Biedl et al.[1] first posed the problem of finding the center of a circle, starting from a point on the boundary, using a limited number of operations. We solve an open problem, presented in their work: finding the center of an ellipse. We present new algorithms for finding the center of the ellipse and provide results of experiments showing how these algorithms perform under the introduction o...
متن کاملon the perimeter of an ellipse
let e be the ellipse with major and minor radii a and b respectively, and pbe its perimeter, then p = lim 4 tan(p/n)(a + b + 2) σ a2 cos2 (2k-2)pi/n+ sin2 (2k-2)pi/n; where n = 2m. so without considering the limit, it gives a reasonable approxi-mation for p, it means that we can choose n large enough such that the amountof error be less than any given small number. on the other hand, the formul...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2010
ISSN: 0377-0427
DOI: 10.1016/j.cam.2009.08.011