New Quadratic Integration

[Namir]

(05-31-2018 02:27 AM)ttw Wrote:  Generally, three point rules like Simpson's are just as good (in order of magnitude) as the one with one more point (Bode's rule in this group.) Thus, another functional evaluation may not be that valuable if used in a simple integration formula.

I agree. I had noticed that Simpron's 1/3 rule is not that inferior to Simpson's 3/8 rule. With the computing power we have we can afford to use Simpron's rules with a high number of interval divisions. We can also use the method I am proposing in this thread. Such a method would have been abandoned my mathematicians who did not have access to computers. They kept their algorithms simple.