Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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
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.

References [Enhancements On Off] (What's this?)

  • [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

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 65R05, 45L10

Retrieve articles in all journals with MSC: 65R05, 45L10

Additional Information

DOI: https://doi.org/10.1090/qam/448967
Article copyright: © Copyright 1975 American Mathematical Society

American Mathematical Society