Discrete Collocation for a First Kind Cauchy Singular Integral Equation with Weakly Singular Solution
نویسندگان
چکیده
منابع مشابه
Solution of a class of the first kind singular integral equation with multiplicative Cauchy kernel
where D = (−1, 1)× (−1, 1) , f(x, y) is a given Hölder continuous function in D, and φ(x, y) is an unknown function. The equation (1) has applications in the theory of aeroelasticity [1]. Note that the equation without logarithmic singularities was many times considered in different classes of functions. In the literature the solutions of the equation (1) in bounded domains [2, 5, 6, 9] as well...
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p(t, s) := s tμ , (1.2) where μ > 0, K(t, s) is a smooth function and g is a given function, can arise, e.g., in heat conduction problems with mixed boundary conditions ([2], [10]). The case when K(t, s) = 1 has been considered in several papers. The following lemma summarizes the analytical results for (1.1) in the case K(t, s) = 1. Lemma 1.1. (a) [12] Let μ > 1 in (1.2). If the function g bel...
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In this work a study of efficient approximate methods for solving the Cauchy type singular integral equations (CSIEs) of the first kind, over a finite interval, is presented. In the solution, Chebyshev polynomials of the first kind, Tn(x)Tn(x), second kind, Un(x)Un(x), third kind, Vn(x)Vn(x), and fourth kind, Wn(x)Wn(x), corresponding to respective weight functions View the MathML sourceW(1)(x)...
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ژورنال
عنوان ژورنال: Journal of Integral Equations and Applications
سال: 1997
ISSN: 0897-3962
DOI: 10.1216/jiea/1181076029