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Simpson's rules are a set of rules used in ship stability and naval architecture, to calculate the areas and volumes of irregular figures. [1] This is an application of Simpson's rule for finding the values of an integral , here interpreted as the area under a curve.
The most basic of these rules, called Simpson's 1/3 rule, or just Simpson's rule, reads [() + (+) + ()]. In German and some other languages, it is named after Johannes Kepler , who derived it in 1615 after seeing it used for wine barrels (barrel rule, Keplersche Fassregel ).
Simpson's rules (ship stability) Simpson–Kramer method This page was last edited on 29 March 2018, at 20:51 (UTC). Text is available under the Creative Commons ...
Simpson's rule, which is based on a polynomial of order 2, is also a Newton–Cotes formula. Quadrature rules with equally spaced points have the very convenient property of nesting. The corresponding rule with each interval subdivided includes all the current points, so those integrand values can be re-used.
The zeroeth extrapolation, R(n, 0), is equivalent to the trapezoidal rule with 2 n + 1 points; the first extrapolation, R(n, 1), is equivalent to Simpson's rule with 2 n + 1 points. The second extrapolation, R(n, 2), is equivalent to Boole's rule with 2 n + 1 points. The further extrapolations differ from Newton-Cotes formulas.
Homer Simpson’s reported decision to stop strangling his son, Bart, has fans talking — at least on the Internet. That’s where everyone, of course, has an opinion. And now, the executive ...
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