Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 

 

On solving singular integral equations via a hyperbolic tangent quadrature rule


Author: Ezio Venturino
Journal: Math. Comp. 47 (1986), 159-167
MSC: Primary 65R20; Secondary 45E05
MathSciNet review: 842128
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We propose a scheme for solving singular integral equations based on a "hyperbolic tangent" quadrature rule. The integral equation is reduced to a system of linear equations, after quadrature and collocation. The matrix of the system is shown to be nonsingular for every choice of the number of quadrature nodes by producing a lower bound for its determinant.


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

  • [1] F. R. Gantmacher, The theory of matrices. Vols. 1, 2, Translated by K. A. Hirsch, Chelsea Publishing Co., New York, 1959. MR 0107649
  • [2] J. McNamee, F. Stenger, and E. L. Whitney, Whittaker’s cardinal function in retrospect, Math. Comp. 25 (1971), 141–154. MR 0301428, 10.1090/S0025-5718-1971-0301428-0
  • [3] R. A. Sack, Comments on some quadrature formulas by F. Stenger, J. Inst. Math. Appl. 21 (1978), no. 3, 359–361. MR 0494861
  • [4] Frank Stenger, Integration formulae based on the trapezoidal formula, J. Inst. Math. Appl. 12 (1973), 103–114. MR 0381261
  • [5] Frank Stenger, Approximations via Whittaker’s cardinal function, J. Approximation Theory 17 (1976), no. 3, 222–240. MR 0481786
  • [6] Frank Stenger, Remarks on “Integration formulae based on the trapezoidal formula” (J. Inst. Math. Appl. 12 (1973), 103–114), J. Inst. Math. Appl. 19 (1977), no. 2, 145–147. MR 0440879
  • [7] F. Stenger & D. Elliott, "SINC method of solution for singular integral equations," in Numerical Solution of Singular Integral Equations (A. Gerasoulis, R. Vichnevetsky, eds.), Proceedings of an IMACS International Symposium held at Lehigh University, Bethlehem, PA, USA, June 21-22, 1984, pp. 27-35.
  • [8] J. M. Whittaker, "On the cardinal function of interpolation theory," Proc. Edinburgh Math. Soc. (1), v. 2, 1927, pp. 41-46.
  • [9] E. Venturino, An Analysis of Some Direct Methods for the Numerical Solution of Singular Integral Equations, Ph. D. thesis, SUNY at Stony Brook, 1984.

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65R20, 45E05

Retrieve articles in all journals with MSC: 65R20, 45E05


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1986-0842128-9
Article copyright: © Copyright 1986 American Mathematical Society