Boole's rule
Encyclopedia
In mathematics, Boole's rule, named after George Boole
, is a method of numerical integration
. It approximates an integral
by using the values of ƒ at five equally spaced points
It is expressed thus Abramowitz and Stegun
(1972, p. 886):
and the error term is
for some number c between x1 and x5. (945 = 1 × 3 × 5 × 7 × 9.)
It is often known as Bode's rule, due to a typographical error in Abramowitz and Stegun
(1972, p. 886) that propagated.
George Boole
George Boole was an English mathematician and philosopher.As the inventor of Boolean logic—the basis of modern digital computer logic—Boole is regarded in hindsight as a founder of the field of computer science. Boole said,...
, is a method of numerical integration
Numerical integration
In numerical analysis, numerical integration constitutes a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations. This article focuses on calculation of...
. It approximates an integral
by using the values of ƒ at five equally spaced points
It is expressed thus Abramowitz and Stegun
Abramowitz and Stegun
Abramowitz and Stegun is the informal name of a mathematical reference work edited by Milton Abramowitz and Irene Stegun of the U.S. National Bureau of Standards...
(1972, p. 886):
and the error term is
for some number c between x1 and x5. (945 = 1 × 3 × 5 × 7 × 9.)
It is often known as Bode's rule, due to a typographical error in Abramowitz and Stegun
Abramowitz and Stegun
Abramowitz and Stegun is the informal name of a mathematical reference work edited by Milton Abramowitz and Irene Stegun of the U.S. National Bureau of Standards...
(1972, p. 886) that propagated.