Simpson’s rule

Simpson’s rule is a method of (approximate) numerical definite integration (or quadratureMathworldPlanetmath). Simpson’s rule is based on a parabolic model of the functionMathworldPlanetmath to be integrated (in contrast to the trapezoidal model of the trapezoidal rule). Thus, a minimum of three points and three function values are required. Here we take three equidistant points: x0x2 the intervalMathworldPlanetmathPlanetmath endpoints, x1=(x0+x2)/2 the midpointMathworldPlanetmathPlanetmathPlanetmath, and let h=|b-a|/2 the distance between each. The definite integral is then approximated by:


We can extend this to greater precision by breaking our target domain into n equal-length fragments. The quadrature is then the weighted sum of the above formula for every pair of adjacentPlanetmathPlanetmath regions, which works out for even n to

Title Simpson’s rule
Canonical name SimpsonsRule
Date of creation 2013-03-22 13:40:12
Last modified on 2013-03-22 13:40:12
Owner drini (3)
Last modified by drini (3)
Numerical id 9
Author drini (3)
Entry type Theorem
Classification msc 28-00
Classification msc 26A06
Classification msc 41A55
Classification msc 65D32
Related topic LagrangeInterpolationFormula
Related topic NewtonAndCotesFormulas
Related topic PrismatoidMathworldPlanetmath