Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-25T04:21:10.715Z Has data issue: false hasContentIssue false
  • English
  • Français

Derivation of correction terms for general quadrature formulae

Published online by Cambridge University Press:  24 October 2008

J. A. Grant
J. A. Grant
Affiliation:
Computing Laboratory, University of Leeds
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, it will be shown how it is possible, using Bernoulli polynomials of the first kind, to derive correction terms for any quadrature approximation in the form of a weighted sum over a finite interval. The terms derived will involve either the difference or the sum of derivatives taken at the ends of the range of integration, and they will be described as being of either Type A or Type B respectively. There will also be some discussion of the uses of such terms.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 66 , Issue 3 , November 1969 , pp. 571 - 586
Copyright
Copyright © Cambridge Philosophical Society 1969

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Davis, H. T.Tables of the higher mathematical functions, Volume 2 (Bloomington, Indiana; Principia Press, 1935).Google Scholar
(2)Fletcher, A., Miller, J. C. P., Rosenhead, L. and Comrie, L. J.An index of mathematical tables, 2nd edition (Scientific Computing Service, 1962).Google Scholar
(3)Krylov, V. I.Approximate calculation of integrals (New York; Macmillan, 1962).Google Scholar
(4)Milne-Thomson, L. M.The calculus of finite differences (London; Macmillan, 1933).Google Scholar