Simpson revival

[Dieter]

(09-28-2016 08:04 AM)Pekis Wrote:  The problem with Simpson's rule for calculating a definite integral is that you have to specify the number of intervals. I surely reinvented the wheel but I found a way to deal with a given tolerance (e.g. 1E-5), WITHOUT wasting any calculation in the process.

As it is the case with most clever ideas, you indeed reinvented the wheel. ;-)
Which of course doesn't make the method less clever.

(09-28-2016 08:04 AM)Pekis Wrote:  What do you think of it ?

It's such an obvious improvement that some time ago I posted a HP41 version of this idea. This program even calculates an improved approximation from the two last Simpson results, using the error estimate associated with this method. For instance, if you have the results for 4 and 8 intervals, you can get a new result from these two, having an accuracy comparable to the result with 16 intervals. What about implemeting this idea in your BASIC program?

A long time ago a much better mathematician had a similar idea based on the trapezoid method combined with an extraordinarily clever extrapolation scheme, leading to what is now known as the Romberg method.

Dieter