New Trapedoizal Tail integration method

[Namir]

(05-13-2021 12:05 PM)Albert Chan Wrote:  

(05-12-2021 06:05 PM)Namir Wrote:  The method samples two function values in each interval at f(x+h/2-h/3) and fx(x+h/2+h/3)

You might also try f(x+h/2 ± h/(2√3))
This is the points and weights for 2 points Gaussian quadrature.

Because 2√3 ≈ 3.464 relatively close to 3, this explained the good result you observed.

Thanks Albert! The 2*sqrt(3) makes sense. I tried several points on either side of the half interval with varying degrees of success.

Namir