New Quadratic Integration

[ttw]

Two questions come to mind. First, what is the error expansion (perhaps by way of a Taylor series), and second, how much doe the method cost. Could the extra cost be used to move to a higher (or extrapolated like Richardson's method) integration method.

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.

Another problem is in round off. At low degree Newton-Cotes formulas, no problems arise but after 8 or so points, the coefficients change sign and get really big.