Open AccessNumerical Differentiation and Integration
Author(s) -
Dragan Obradović,
Lakshmi Narayan Mishra,
Vishnu Narayan Mishra
Publication year - 2021
Publication title -
journal of advances in physics
Language(s) - English
Resource type - Journals
ISSN - 2347-3487
DOI - 10.24297/jap.v19i.8938
Subject(s) - numerical integration , numerical differentiation , elementary function , function (biology) , computer science , numerical analysis , mathematics , directional derivative , derivative (finance) , mathematical optimization , calculus (dental) , mathematical analysis , medicine , dentistry , evolutionary biology , financial economics , economics , biology
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.