What difference Between Simpsons Rule and 3

Esmeralda Lane

Esmeralda Lane

Answered question

2022-07-02

What difference Between Simpsons Rule and 3 / 8 rule?

Answer & Explanation

Brendan Bush

Brendan Bush

Beginner2022-07-03Added 14 answers

There are two advantages of the 3/8ths rule: First, the error term is smaller than Simpson's rule.
The second more important use of the 3/8ths rule is for uniformly sampled function integration. Suppose you have a function known at equally spaced points. If the number of points is odd, then the composite Simpson's rule works just fine. If the number of points is even, then you have a problem at the end. One solution is to use the 3/8ths rule. For example, if the user passed 6 samples, then you use Simpson's for the first three points, and 3/8ths for the last 4 (the middle point is common to both). This preserves the order of accuracy without putting an arbitrary constraint on the number of samples.

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