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.

**[1]**F. Erdogan and G. D. Gupta,*On the numerical solution of singular integral equations*, Quart. Appl. Math.**30**, 525 (1972) MR**0408277****[2]**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 MR**0471394****[3]**N. I. Muskhelishvili,*Singular integral equations*, Wolters-Noordhoff Publishing, Groningen, 1958 MR**0438058****[4]**F. G. Tricomi,*On the finite Hilbert transformation*, Quart. J. Math. Oxford**2**, 199 (1951) MR**0043258****[5]**M. Abramowitz and I. A. Stegun,*Handbook of mathematical functions*, Dover Publications, Inc., New York, 1965**[6]**A. H. Stroud and Don Secrest,*Gaussian quadrature formulas*, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1966 MR**0202312****[7]**S. Krenk,*A note on the use of the interpolation polynomial for solutions of singular integral equations*, to appear in Quart. Appl. Math. MR**0474919****[8]**L. V. Kantorovich and V. I. Krylov,*Approximate methods of higher analysis*, Noordhoff, Groningen, 1964

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DOI:
https://doi.org/10.1090/qam/448967

Article copyright:
© Copyright 1975
American Mathematical Society