In numerical analysis, Simpson's rule is a method for numerical integration, the numerical approximation of definite integrals. Specifically, it is the following approximation:
Simpson's rule also corresponds to the 3-point Newton-Cotes quadrature rule.
The method is credited to the mathematician Thomas Simpson (1710–1761) of Leicestershire, England. Kepler used similar formulas over 100 years prior and in German the method is sometimes called Keplersche Fassregel for this reason.
Simpson's rule is a staple of scientific data analysis and engineering. It is widely used, for example, by Naval architects to numerically integrate hull offsets and cross-sectional areas to determine volumes and centroids of ships or lifeboats.
Read more about Simpson's Rule: Error, Composite Simpson's Rule, Alternative Extended Simpson's Rule, Simpson's 3/8 Rule, Sample Implementation
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