, Volume 7, Issue 1, pp 2129
First online:
Numerical solution of Cauchy type singular integral equations with logarithmic weight, based on arbitrary collocation points
 A. C. ChrysakisAffiliated withSection of Mechanics, Department of Engineering Science, The National Technical University of Athens
 , G. TsamasphyrosAffiliated withSection of Mechanics, Department of Engineering Science, The National Technical University of Athens
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Singular integral equations with a Cauchy type kernel and a logarithmic weight function can be solved numerically by integrating them by a Gausstype quadrature rule and, further, by reducing the resulting equation to a linear system by applying this equation at an appropriate number of collocation points x _{k}. Until now these x _{k} have been chosen as roots of special functions. In this paper, an appropriate modification of the original method permits the arbitrary choice of x _{k} without any loss in the accuracy. The performance of the method is examined by applying it to a numerical example and a plane crack problem.
 Title
 Numerical solution of Cauchy type singular integral equations with logarithmic weight, based on arbitrary collocation points
 Journal

Computational Mechanics
Volume 7, Issue 1 , pp 2129
 Cover Date
 199001
 DOI
 10.1007/BF00370054
 Print ISSN
 01787675
 Online ISSN
 14320924
 Publisher
 SpringerVerlag
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 Authors

 A. C. Chrysakis ^{(1)}
 G. Tsamasphyros ^{(1)}
 Author Affiliations

 1. Section of Mechanics, Department of Engineering Science, The National Technical University of Athens, 5, Heroes of Polytechnion Avenue, GR15773, Athens, Greece