Simpson's 3/8 Rule
Simpson's 3/8 rule is another method for numerical integration proposed by Thomas Simpson. It is based upon a cubic interpolation rather than a quadratic interpolation. Simpson's 3/8 rule is as follows:
where b - a = 3h. The error of this method is:
where is some number between and . Thus, the 3/8 rule is about twice as accurate as the standard method, but it uses one more function value. A composite 3/8 rule also exists, similarly as above.
Read more about this topic: Simpson's Rule
Famous quotes containing the words simpson and/or rule:
“In my grandmother’s house there was always chicken soup
And talk of the old country—mud and boards,
Poverty,
The snow falling down and necks of lovers.”
—Louis Simpson (b. 1923)
“Here’s the rule for bargains: “Do other men, for they would do you.” That’s the true business precept.”
—Charles Dickens (1812–1870)