A Pair of Dual Integral Equations Occurring in Diffraction Theory
نویسندگان
چکیده
منابع مشابه
Approximate solution of dual integral equations
We study dual integral equations which appear in formulation of the potential distribution of an electrified plate with mixed boundary conditions. These equations will be converted to a system of singular integral equations with Cauchy type kernels. Using Chebyshev polynomials, we propose a method to approximate the solution of Cauchy type singular integral equation which will ...
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A system of difference equations of the first order with meromorphic coefficients (not necessary periodic ones) subject to certain conditions of symmetry is analysed. These conditions arise in model problems of diffraction theory. A method for the constructive solution of the system of difference equations is proposed. It consists of three steps. First, it requires factorization of a certain fu...
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Dual integral equations with trigonometric kernel are reinvestigated here for a solution. The behaviour of one of the integrals at the end points of the interval complementary to the one in which it is defined plays the key role in determining the solution of the dual integral equations. The solution of the dual integral equations is then applied to find an exact solution of the water wave scat...
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1 Kasner, "Algebraic Potential Curves," BuO. Am. Math. Soc., 1901. 2 Kasner, "Conformal Geometry," Proc. Fifth Internat. Cong. of Math., 2, 81 (1912). 3 Kasner, "Geometry of Conformal Symmetry (Schwarzian Reflection)," Ann. Math., 38, 873 (1937). 4 Comenetz, "Conformal Geometry on a Surface," Ibid., 39, 863 (1938). I wish to thank J. De Cicco, Aida Kailish, F. Supnik and C. Vlucay for assistanc...
متن کاملapproximate solution of dual integral equations
we study dual integral equations which appear in formulation of the potential distribution of an electrified plate with mixed boundary conditions. these equations will be converted to a system of singular integral equations with cauchy type kernels. using chebyshev polynomials, we propose a method to approximate the solution of cauchy type singular integral equation which will ...
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ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 1962
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s0013091500014784