Simpson's Rule Implementation trick?

[Namir]

(03-19-2016 06:45 AM)Dieter Wrote:  

(03-19-2016 04:59 AM)ttw Wrote:  Romberg's method is pretty good. It can be of arbitrarily high order if the integrand is smooth enough and can be adapted to giving error estimates.

This is also possible with Simpson's method. Two approximations with n and 2n intervals give a new and improved estimate.
Take a look a this thread in the HP41 software library.

Dieter

I have implemented a variant of the Romberg method that uses Simpson's rule to start with instead of teh Trapezoidal rule. You can find this variant method on my web site.

Namir