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Numerical solution of Cauchy type singular integral equations with logarithmic weight, based on arbitrary collocation points
 A. C. Chrysakis,
 G. Tsamasphyros
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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.
Communicated by D. E. Beskos, March 8, 1990
 Danloy, B. (1973): Numerical construction of Gaussian quadrature formulas for 291. Math. Comput. 27, 861–869
 Erdogan, F.; Gupta, G. D.; Cook, T. S. (1973): Numerical solution of singular integral equations. In: Sih, G. C. (ed): Mechanics of fracture, vol. 1, Leyden: Noordhoff
 Erdogan, F.; Biricikoglu, V. (1973): Two bonded half planes with a crack going through the interface. Int. J. Eng. Sci. 11, 745–766
 Erdogan, F.; Cook, T. S. (1974): Antiplane shear crack terminating at and going through a bimaterial interface. Int. J. Fract. 10, 227–240
 Junghanns, P.; Silbermann, B. (1981): Zur Theorie der Näherung verfahren für singuläre Integralgleichungen auf Intervallen. Math. Nachr. 103, 199–244
 Ioakimidis, N. I. (1976): General methods for the solution of crack problems in the theory of plane elasticity. Doctoral Thesis at the National Technical University of Athens, Greece. Univ. Microfilms order no. 7621, 056
 Ioakimidis, N. I. (1980): The numerical solution of crack problems in plane elasticity in the case of loading discontinuities. Eng. Fract. Mech. 13, 709–716
 Ioakimidis, N. I. (1981): On the natural interpolation formula for Cauchy type integral equations of the first kind. Computing 26, 73–77
 Ioakimidis, N. I. (1984): Application of interpolation formulas to the numerical solution of singular integral equations. Serdica 10, 78–87
 Ioakimidis, N. I.; Theocaris, P. S. (1980): On the selection of collocation points for the numerical solution of singular integral equations with generalized kernels appearing in elasticity problems. Comput. Struct. 11, 289–295
 Kulich, N. V. (1974): The computation of certain Cauchytype integrals and singular integrals with logarithmic singularities. Versi Akademii Navuk BSSRSeriya FizikaMatematychnykh 1, 90–94
 Muskhelishvili, N. I. (1975): Some basic problems of the mathematical theory of elasticity. Leyden: Noordhoff
 Stroud, A. H.; Secrest D. (1966): Gaussian quadrature formulas. Englewood, Cliffs, NJ: PrenticeHall
 Theocaris, P. S.; Chrysakis, A. C.; Ioakimidis, N. I. (1979): Cauchytype integrals and integral equations with logarithmic singularities. J. Eng. Math. 13, 63–74
 Tsamasphyros, G.; Theocaris, P. S. (1976): Sur une méthode génerale de quadrature des integrales du type Cauchy. Balkan Conference of Applied Mathematics in Salonica.
 Tsamasphyros, G.; Theocaris, P. S. (1979): Numerical solution of systems of singular equations with variable coefficients. Appl. Anal. 7, 37–52
 Tsamasphyros, G.; Theocaris, P. S. (1981a); Are special collocation points necessary for the numerical solution of singular integral equations? Int. J. Fract. 17, R21R24.
 Tsamasphyros, G.; Theocaris, P. S. (1981b): Equivalence and convergence of direct and indirect methods for the numerical solution of singular integral equations. Computing 27, 71–80
 Tsamasphyros, G. (1986): A study of factors influencing the solution of singular integral equations. Eng. Fract. Mech. 24, 567–578
 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
 19900101
 DOI
 10.1007/BF00370054
 Print ISSN
 01787675
 Online ISSN
 14320924
 Publisher
 SpringerVerlag
 Additional Links
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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