Numerical Differentiation and Integration
Keywords:Special cases of Newton-Cotes formulas., Newton-Cotes formulas, numerical differentiation, numerical integration
There are several reasons why numerical differentiation and integration are used. The function that integrates f (x) can be known only in certain places, which is done by taking a sample. Some supercomputers and other computer applications sometimes need numerical integration for this very reason. The formula for the function to be integrated may be known, but it may be difficult or impossible to find the antiderivation that is an elementary function. One example is the function f (x) = exp (−x2), an antiderivation that cannot be written in elementary form. It is possible to find antiderivation symbolically, but it is much easier to find a numerical approximation than to calculate antiderivation (anti-derivative). This can be used if antiderivation is given as an unlimited array of products, or if the budget would require special features that are not available to computers.
R.P. Agarwal and P.J.Y. Wong, ET-TOT Inequalities in Polynomial Interpolation and Their Applications, Kluwer Academic Publishers, Boston, MA, (1993).
Gradimir V. Milovanovi, Numerical Analysis Part I, Scientific Book, Belgrade, 1991.
Gradimir V. Milovanovi, Numerical Analysis Part II, Scientific Book, Belgrade, 1991.
S. P. Venkateshan, “Numerical Integration”, in: S. P. Venkateshan and P. Swaminathan (eds.), Computational Methods in Engineering, 1st edition, pp 317-373. Oxford, UK: Academic Press, 2013.
Jovanovic B., Radunovic D., Numerical Analysis, Faculty of Mathematics, 2003.
Marchuk GI, Methods of numerical mathematics (rus.), Nauka, Moscow, 1980.
Bertolino, M. Numerical Analysis. Scientific book, Belgrade, 1981.
E.T. Whittaker and G. Robinson, "The Newton-Cotes Formulae of Integration." 76 in The Calculus of Observations: A Treatise on Numerical Mathematics, 4th ed. New York: Dover, pp.152-156, 1967
Wikipedia Newton Cotes formulas, (Available at:
Wolfram Mathworld Newton Cotes formulas, (Available at: http://mathworld.wolfram.com/Newton-CotesFormulas.html)
I.R. Khan, R. OhbaNew finite difference formulas for numerical differentiation Journal of Computational and Applied Mathematics, 126 (2000), pp. 269-276
How to Cite
Copyright (c) 2021 Dragan Obradovic, Lakshmi Narayan Mishra, Vishnu Narayan Mishra
This work is licensed under a Creative Commons Attribution 4.0 International License.
All articles published in Journal of Advances in Linguistics are licensed under a Creative Commons Attribution 4.0 International License.