Stoney units

In mathematics, Boole's rule, named after George Boole, is a method of numerical integration. It approximates an integral

$\underset{x_1}{\overset{x_5}{\int }}f(x)dx$

by using the values of ƒ at five equally spaced points

$x_1,x_2=x_1+h,x_3=x_1+2h,x_4=x_1+3h,x_5=x_1+4h.$

It is expressed thus Abramowitz and Stegun (1972, p. 886):

$\underset{x_1}{\overset{x_5}{\int }}f(x)dx=\frac{2h}{45}(7f(x_1)+32f(x_2)+12f(x_3)+32f(x_4)+7f(x_5))+\text{error term},$

and the error term is

$-\frac{8}{945}{h}^7{f}^{(6)}(c)$

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 that propagated; e.g. in Abramowitz and Stegun (1972, p. 886).

See also

• Newton-Cotes formulas
• Simpson's Rule
• Romberg's method

References

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