On quadrature formulas for singular integral equations of the first and the second kind

Krenk, Steen

doi:10.1090/qam/448967

Author: Steen Krenk
Journal: Quart. Appl. Math. 33 (1975), 225-232
MSC: Primary 65R05; Secondary 45L10
DOI: https://doi.org/10.1090/qam/448967
MathSciNet review: 448967
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper it is shown that by proper choice of the collocation points singular integral equations of the first and the second kind can be integrated by use of the usual Gauss-Jacobi quadrature formula. Detailed formulas are given for various values of the index.

F. Erdogan and G. D. Gupta, On the numerical solution of singular integral equations, Quart. Appl. Math. 29 (1971/72), 525–534. MR 408277, DOI https://doi.org/10.1090/S0033-569X-1972-0408277-4
F. Erdogan, G. D. Gupta, and T. S. Cook, Numerical solution of singular integral equations, Mechanics of fracture, Vol. 1, Noordhoff, Leiden, 1973, pp. 368–425. MR 0471394
N. I. Muskhelishvili, Singular integral equations, Noordhoff International Publishing, Leyden, 1977. Boundary problems of function theory and their application to mathematical physics; Revised translation from the Russian, edited by J. R. M. Radok; Reprinted of the 1958 edition. MR 0438058
F. G. Tricomi, On the finite Hilbert transformation, Quart. J. Math. Oxford Ser. (2) 2 (1951), 199–211. MR 43258, DOI https://doi.org/10.1093/qmath/2.1.199

M. Abramowitz and I. A. Stegun, Handbook of mathematical functions, Dover Publications, Inc., New York, 1965

A. H. Stroud and Don Secrest, Gaussian quadrature formulas, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1966. MR 0202312
Steen Krenk, On the use of the interpolation polynomial for solutions of singular integral equations, Quart. Appl. Math. 32 (1974/75), 479–484. MR 474919, DOI https://doi.org/10.1090/S0033-569X-1975-0474919-7

L. V. Kantorovich and V. I. Krylov, Approximate methods of higher analysis, Noordhoff, Groningen, 1964