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Simpson's 1/3 rule, also simply called Simpson's rule, is a method for numerical integration proposed by Thomas Simpson. It is based upon a quadratic interpolation and is the composite Simpson's 1/3 rule evaluated for n = 2 {\\displaystyle n=2} .
For instance, in the latter, Simpson's 3rd rule is used to find the volume between two co-ordinates. To calculate the entire area / volume, Simpson's first rule is used. [7] Simpson's rules are used by a ship's officers to check that the area under the ship's GZ curve complies with IMO stability criteria.
Adaptive Simpson's method, also called adaptive Simpson's rule, is a method of numerical integration proposed by G.F. Kuncir in 1962. [1] It is probably the first recursive adaptive algorithm for numerical integration to appear in print, [ 2 ] although more modern adaptive methods based on Gauss–Kronrod quadrature and Clenshaw–Curtis ...
Polynomial interpolation also forms the basis for algorithms in numerical quadrature (Simpson's rule) and numerical ordinary differential equations (multigrid methods). In computer graphics , polynomials can be used to approximate complicated plane curves given a few specified points, for example the shapes of letters in typography .
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Download QR code; Print/export Download as PDF; ... move to sidebar hide. See: Simpson's rule, a method of numerical integration; Simpson's rules (ship stability) ...
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.
Thomas Simpson FRS (20 August 1710 – 14 May 1761) was a British mathematician and inventor known for the eponymous Simpson's rule to approximate definite integrals. The attribution, as often in mathematics, can be debated: this rule had been found 100 years earlier by Johannes Kepler , and in German it is called Keplersche Fassregel , or ...