Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

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



Two formulas for numerical indefinite integration

Author: Seymour Haber
Journal: Math. Comp. 60 (1993), 279-296
MSC: Primary 65D32; Secondary 41A55
MathSciNet review: 1149292
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We derive two formulas for approximating the indefinite integral over a finite interval. The approximation error is $ O({c^{ - c\sqrt m }})$ uniformly, where m is the number of integrand evaluations. The integrand is required to be analytic in the interior of the integration interval, but may be singular at the endpoints. Some sample calculations indicate that the actual convergence rate accords with the error bound derived.

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

  • [1] M. Abramowitz and I. A. Stegun, Eds., Handbook of Mathematical Functions, U.S. Government Printing Office, Washington, DC, 1964, Fomulas 5.2.8, 5.2.34, and 5.2.35. MR 0167642 (29:4914)
  • [2] S. Haber, The tanh rule for numerical integration, SIAM J. Numer. Anal. 14 (1977), 668-685. MR 0448818 (56:7123)
  • [3] R.B. Kearfott, A Sinc approximation for the indefinite integral, Math. Comp. 41 (1983), 559-572. MR 717703 (85g:65029)
  • [4] J. McNamee, F. Stenger, and E. L. Whitney, Whittaker's cardinal function in retrospect, Math. Comp. 25 (1971), 141-154. MR 0301428 (46:586)
  • [5] K. Sikorski and F. Stenger, Optimal quadratures in $ {H_p}$ spaces, ACM Trans. Math. Software 10 (1984), 140-151. MR 791982 (87a:65054a)
  • [6] I. A. Stegun and R. Zucker, Automatic computing methods for special functions, Part III. The Sine, Cosine, Exponential integrals and related functions, J. Res. Nat. Bur. Standards B, Mathematical Sciences 80B (1976), 291-311. MR 0428687 (55:1707)
  • [7] F. Stenger, Numerical methods based on Whittaker cardinal, or Sinc functions, SIAM Rev. 23 (1981), 165-224. MR 618638 (83g:65027)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65D32, 41A55

Retrieve articles in all journals with MSC: 65D32, 41A55

Additional Information

Article copyright: © Copyright 1993 American Mathematical Society

American Mathematical Society