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Formulae for Numerical Differentiation

Published online by Cambridge University Press:  03 November 2016

W G. Bickley
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In a recent paper (1) formulae were given for the numerical integration of a function in terms of its values at a set of arguments at equal intervals. In this companion paper, formulae for numerical differentiation, using the same data, are collected. Their utility in enabling derivatives of a function given numerically at such a set of arguments to be computed is obvious, the need arises in several approximate methods which are coming more and more into use (2), (3). The formulae avoid the labour of preliminary differencing, and are indeed more convenient than the finite difference formulae when the derivative is required at all the points of subdivision of a limited range.

Type
Research Article
Information
The Mathematical Gazette , Volume 25 , Issue 263 , February 1941 , pp. 19 - 27
Copyright
Copyright © Mathematical Association 1941

References

(1) Bickley, W. G., “Formulae for Numerical Integration”. Math. Gazette, XXIII, pp. 352–359, Oct. 1939.CrossRefGoogle Scholar
(2) Bradfield, K. N. E. and Southwell, R. V., “Relaxation Methods Applied to Engineering Problems”. Proc. Roy. Soc., A, 161, pp. 155–181, July 1937.Google Scholar
(3) Crout, P. D., “An Application of Polynomial Approximation to the Solution of Integral Equations arising in Physical Problems”. J. Math. and Phys., XIX, pp. 34–91, Jan. 1940. (Crout gives coefficients for m = 1, 2, and 3, with n = 2, 4, and 6.)CrossRefGoogle Scholar