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Gauss-type quadratures for weakly singular integrals and their application to Fredholm integral equations of the second kind

Authors: Hideaki Kaneko and Yuesheng Xu
Journal: Math. Comp. 62 (1994), 739-753
MSC: Primary 65D32; Secondary 45L10, 65R20
MathSciNet review: 1218345
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Abstract: In this paper we establish Gauss-type quadrature formulas for weakly singular integrals. An application of the quadrature scheme is given to obtain numerical solutions of the weakly singular Fredholm integral equation of the second kind. We call this method a discrete product-integration method since the weights involved in the standard product-integration method are computed numerically.

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Keywords: Gaussian quadrature, singular integrals, weakly singular Fredholm integral equations, product-integration scheme
Article copyright: © Copyright 1994 American Mathematical Society