Numerical integration is the term used for a number of methods to find an approximation for an integral. Numerical integration has also been called quadrature. Very often, it is not possible to solve integration analytically, for example when the data consists of a number of distinct measurements, or when the antiderivative is not known, and it is difficult, impractical or impossible to find it. In such cases, the integral can be written as a mathematical function defined over the interval in question, plus a function giving the error.
Various formulas have been studied for many years and become famous. For example, there is the Gaussian quadrature (named after Gauss), the Newton-Cotes formula (named after Isaac Newton), and the Euler-Maclaurin formula (named after Leonhard Euler).
Numerical errors[change | change source]
People who studied about numerical integration[change | change source]
References[change | change source]
- Davis, P. J., & Rabinowitz, P. (2007). Methods of numerical integration. Courier Corporation.
- Weisstein, Eric W. "Gaussian Quadrature." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GaussianQuadrature.html
- Weisstein, Eric W. "Newton-Cotes Formulas." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Newton-CotesFormulas.html
- Weisstein, Eric W. "Euler-Maclaurin Integration Formulas." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Euler-MaclaurinIntegrationFormulas.html
- Rump, S. M. (2010). Verification methods: Rigorous results using floating-point arithmetic. Acta Numerica, 19, 287-449.
Numerical integration software[change | change source]
- MATLAB, INTLAB
- Wolfram Mathematica - made by Wolfram Research
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