Lecture 23.
Today we looked at errors of integration
for the Newton Cotes rules. We saw why the midpoint rule is as accurate as the
trapezoid rule, and Simpson's rule is as accurate as a rule using a cubic
interpolating polynomial. We also looked at composite rules, in particular we
explored using a composite Simpson's rule on multiple panels.
If you are trying to follow
the algebra in Recktenwald consult the errata page. In particular there are
multiple errors in equation (11.9) on page 613 that may trip you up.
On Friday we will look at
adaptive algorithms for solving integrals.
Posted: Wed - November 1, 2006 at 12:05 PM