Simpson’s rule

Transcribed from the printed issue; not yet reviewed. Read it in the PDF of the issue, page 19

In the Education Vector for October, Professor Tony O’Hagan makes out a heuristic case for a version of the trapezium rule rather than Simpson’s rule when integrating over more than three points. His argument is appealing but, unfortunately, wrong.

The rule which Professor O’Hagan advocates is equivalent to a pair of Simpson’s rule estimates across the body of the integral together with “a bit of trapezium rule on the first and last intervals”. It is these bits of trapezium rule which cause the problems. They have errors proportional to h3 , (where h is the strip width) while the Simpson’s rules have errors proportional to h4. It follows that, for small enough h, the errors in the bits of trapezium rule must dominate, and hence that Professor O’Hagan’s rule must perform less well than Simpson’s rule.

So Simpson’s rule is saved - though I would hope that those doing numerical integration would go further and use Romberg’s method which can be extrapolated to any required degree of accuracy.

[Tony O’Hagan acknowledges the error, and retracts his criticism - Ed.]