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A. V. Andreev, "Direct numerical method for solving singular integral equations of the first kind with generalized kernels," Mech. Solids. 40 (1), 104-119 (2005)
Year 2005 Volume 40 Number 1 Pages 104-119
Title Direct numerical method for solving singular integral equations of the first kind with generalized kernels
Author(s) A. V. Andreev (Moscow)
Abstract The present paper is devoted to the development of methods for direct numerical solution of a singular integral equation (SIE) of the first kind with the Cauchy-type kernel. The case is considered in which, at the ends of the integration interval, the solution of the SIE has power-law asymptotics, for example, arbitrary (integrable) real-valued singularities.
References
1.  F. E. Erdogan, G. D. Gupta, and T. S. Cook,"The numerical solutions of singular integral equations," in Mechanics of Fracture. Volume 1. Methods of Analysis and Solutions of Crack Problems, pp. 368-425, Noordhoff, Leyden, 1973.
2.  N. I. Muskhelishvili, Singular Integral Equations [in Russian], Nauka, Moscow, 1968.
3.  A. I. Kalandiya, Mathematical Methods of Two-dimensional Elasticity [in Russian], Nauka, Moscow, 1973.
4.  M. P. Savruk, Two-dimensional Elasticity Problems for Bodies with Cracks [in Russian], Naukova Dumka, Kiev, 1981.
5.  R. V. Dubuchava, "Integral convolution equations with discontinuous fore-symbols, singular integral equations with fixed singularities, and their applications to mechanical problems," in Trudy Tbil. Mat. In-ta AN GSSR, Vol. 60, 1979.
6.  P. S. Theocaris and N. I. Ioakimidis, "The V-notched elastic half-plane problem," Acta Mech., Vol. 32, No. 1-3, pp. 125-140, 1979.
7.  M. L. Williams, "Stress singularities resulting from various boundary conditions in angular corners of plates in extension," J. Appl. Mech., Vol. 19, No. 4, pp. 526-528, 1952.
8.  A. I. Kalandiya, "Comments on the singularity of elastic solutions near corners," PMM [Applied Mathematics and Mechanics], Vol. 33, No. 1, pp. 132-135, 1969.
9.  A. V. Andreev, R. V. Goldstein, and Yu. V. Zhitnikov, "Asymptotic analysis of a solution in the vicinity of a kink point of an interface crack," PMM [Applied Mathematics and Mechanics], Vol. 63, No. 5, pp. 865-870, 1999.
10.  C. Laurita, "Condition numbers for singular inegral equations in weighted L2 spaces," J. Comput. and Appl. Math., Vol. 116, No. 1, pp. 23-40, 2000.
11.  K. Chen, "Efficient iterative solution of linear systems from discretizing singular integral equations," Electronic Trans. on Numer. Analysis, Vol. 2, pp. 76-91, 1994.
12.  G. Szegö, Orthogonal Polynomials [Russian translation], Fizmatgiz, Moscow, 1962.
13.  W. Gautschi, "Gauss-Radau formulae for Jacobi and Lguerre weight functions," Mathematics and Computers in Simulation, Vol. 54, No. 4-5, pp. 403-412, 2000.
14.  M. Kzaz, "Convergence acceleration of Jacobi-Gauss quadrature formulae for analytic functions with poles," J. Comput. and Appl. Math., Vol. 57, No. 1-2, pp. 181-192, 1995.
15.  P. Kim and S. Lee, "A piecewise linear quadrature of Cauchy singular integrals," J. Comput. and Appl. Math., Vol. 95, No. 1-2, pp. 101-105, 1998.
16.  P. Kim and U. J. Choi, "A quadrature rule for weighted Cauchy integrals," J. Comput. and Appl. Math., Vol. 126, No. 1-2, pp. 221-232, 2000.
17.  P. S. Theocaris and N. I. Ioakimidis, "Stress intensity factors at the tips of an antiplane shear crack terminating at a bimaterial interface," Intern. J. Fracture., Vol. 13, No. 4, pp. 549-552, 1977.
18.  A. V. Andreev, A Method for the Numerical Solution of a Singular Integral Equation of the First Kind with a Generalized Cauchy-type Kernel. Preprint No. 743 [in Russian], In-t Problem Mekhaniki RAN, Moscow, 2004.
19.  M. M. Chawla and T. R. Ramacrihnan, "Modified Gauss-Jacobi quadrature formulas for the numerical evaluation of Cauchy type singular integrals," BIT, Vol. 14, No. 1, pp. 14-21, 1974.
20.  A. V. Andreev, "Limiting equilibrium analysis of curvilinear boundary cracks in an elastic half-plane, with the stress asymptotic behavior being taken into account," Izv. AN. MTT [Mechanics of Solids], No. 6, pp. 82-96, 2003.
21.  A. F. Nikiforov and V. B. Uvarov, Special Functions of Mathematical Physics [in Russian], Nauka, Moscow, 1984.
22.  A. H. Stroud and D. Secrest, Gaussian Quadrature Formulas, Prentice-Hall, New Jersey, 1966.
23.  C. J. Lanczos, "A precision approximation of the gamma function," SIAM J. Numer. Anal. Ser. B., Vol. 1, pp. 86-96, 1964.
24.  Y. L. Luke, The Special Functions and their Approximations. Volume 1, Acad. Press, New York, 1969.
25.  I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Sums, Series, and Products [in Russian], Nauka, Moscow, 1971.
26.  D. Eliott, "Uniform asymptotic expansions of the Jacobi polynomials and an associated function," Math. Comput., Vol. 25, No. 114, pp. 309-315, 1971.
27.  W. Gautchi, "Gauss quadrature approximations to hypergeometric and confluent hypergeometric functions," J. Comput. and Appl. Math., Vol. 139, No. 1, pp. 173-187, 2002.
28.  L. V. Kantorovich and V. I. Krylov, Approximate Methods of Higher Analysis [in Russian], Fizmatgiz, Moscow, Lenigrad, 1962.
29.  H. F. Bueckner, "On a class of singular integral equations," J. Math. Analys. and Appl., Vol. 14, No. 3, pp. 392-426, 1996.
30.  N. S. Bakhvalov, N. P. Zhidkov, and G. M. Kobel'kov, Numerical Methods [in Russian], Nauka, Moscow, 1987.
31.  V. F. Kolmogortsev, G. Ya. Popov, and M. V. Radiollo, "Internal contact between an elastic hollow disk and an infinite plate with a circular cut and a radial crack," Izv. AN SSSR. MTT [Mechanics of Solids], No. 6, pp. 71-82, 1978.
32.  A. V. Andreev, R. V. Goldstein, and Yu. V. Zhitnikov, "Calculation of the limit equilibrium of internal and boundary cracks with interacting surfaces in an elastic half-plane," Izv. AN. MTT [Mechanics of Solids], No. 4, pp. 96-112, 2002.
Received 09 December 2003
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