Simpson's Rule
Jump to navigation
Jump to search
A Simpson's Rule is a Numerical Analysis that ...
- See: Definite Integral, Johannes Kepler, Numerical Analysis, Numerical Integration, Newton–Cotes Formulas, Thomas Simpson.
References
2017
- (Wikipedia, 2017) ⇒ https://en.wikipedia.org/wiki/Simpson's_rule Retrieved:2017-9-16.
- In numerical analysis, Simpson's rule is a method for numerical integration, the numerical approximation of definite integrals. Specifically, it is the following approximation: : [math]\displaystyle{ \int_{a}^{b} f(x) \, dx \approx \tfrac{b-a}{6}\left[f(a) + 4f\left(\tfrac{a+b}{2}\right)+f(b)\right], }[/math] for points that are equally spaced. For unequally spaced points, see Cartwright.
Simpson's rule also corresponds to the three-point Newton-Cotes quadrature rule.
The method is credited to the mathematician Thomas Simpson (1710–1761) of Leicestershire, England. Johannes Kepler used similar formulas over 100 years prior. For this reason the method is sometimes called Kepler's rule, or Keplersche Fassregel in German.
- In numerical analysis, Simpson's rule is a method for numerical integration, the numerical approximation of definite integrals. Specifically, it is the following approximation: : [math]\displaystyle{ \int_{a}^{b} f(x) \, dx \approx \tfrac{b-a}{6}\left[f(a) + 4f\left(\tfrac{a+b}{2}\right)+f(b)\right], }[/math] for points that are equally spaced. For unequally spaced points, see Cartwright.