Simpson's Rule - Simpson's 3/8 Rule

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:

$\int_{a}^{b} f(x) \, dx \approx \frac{3h}{8}\left = \frac{(b-a)}{8}\left\, ,$

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.

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