New Quadratic Integration

[Namir]

(05-31-2018 02:27 AM)ttw Wrote:  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.

I have tackled the issue of enhancing the Romberg method by replacing the initial guess for the integral that uses the Trapezoidal method with using Simpson's rule. The enhanced version of Romberg works better. Locate the link "A New Face of Romberg Integration" on this link. The link right next to it offers an Excel file that shows the VBA code for the enhanced Romberg.

Namir