On quadrature formulas for singular integral equations of the first and the second kind
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
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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
F. Erdogan and G. D. Gupta, On the numerical solution of singular integral equations, Quart. Appl. Math. 30, 525 (1972)
F. Erdogan, G. D. Gupta and T. S. Cook, Numerical solution of singular integral equations, in Methods of analysis and solutions of crack problems, G. C. Sih, ed., Noordhoff Leyden, 1973
N. I. Muskhelishvili, Singular integral equations, Wolters-Noordhoff Publishing, Groningen, 1958
F. G. Tricomi, On the finite Hilbert transformation, Quart. J. Math. Oxford 2, 199 (1951)
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
S. Krenk, A note on the use of the interpolation polynomial for solutions of singular integral equations, to appear in Quart. Appl. Math.
L. V. Kantorovich and V. I. Krylov, Approximate methods of higher analysis, Noordhoff, Groningen, 1964
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Article copyright:
© Copyright 1975
American Mathematical Society