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On the convergence of a Gauss quadrature rule for evaluation of Cauchy type singular integrals. (English) Zbl 0391.65004


MSC:

65D32 Numerical quadrature and cubature formulas
41A55 Approximate quadratures
30E20 Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane
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References:

[1] D. F. Paget and D. Elliott,An algorithm for the numerical evaluation of certain Cauchy principal value integrals, Numer. Math. 19 (1972), 373–385. · Zbl 0229.65091 · doi:10.1007/BF01404920
[2] M. M. Chawla and T. R. Ramakrishnan,Modified Gauss-Jacobi quadrature formulas for the numerical evaluation of Cauchy type singular integrals, BIT 14 (1974), 14–21. · Zbl 0272.65015 · doi:10.1007/BF01933113
[3] G. Tsamasphyros and P. S. Theocaris,Sur une méthode générale de quadrature pour des integrales du type Cauchy, Symposium of Applied Mathematics, Salonica (16–21 August 1976).
[4] P. S. Theocaris and G. Tsamasphyros,Numerical Solution of Systems of Singular Integral Equations with Variable Coefficients, Quart. Appl. Math. (to appear). · Zbl 0404.65068
[5] D. Elliott and D. F. Paget,On the convergence of a quadrature rule for evaluating certain Cauchy principal value integrals, Numer. Math. 23 (1975), 311–319. · Zbl 0313.65019 · doi:10.1007/BF01438258
[6] G. Szegö,Orthogonal Polynomials, American Math. Soc. Colloquium publications, New York (1959).
[7] N. I. Muskhelishvili,Singular Integral Equations, P. Noordhoff N.V., Groningen, Holland (1958).
[8] A. I. Kalandiya,Mathematical Methods of two-dimensional elasticity, Moscow, Mir Publishers (1975). · Zbl 0412.73008
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