- A very convenient way of evaluating integrals
is to repeatedly apply Simpson's rule---halving interval each
time.
- The point is that, as diagram indicates, one
need only evaluate half as many (x in diagram) functions as
you expect because you use old values ( in figure).
- As the error is proportional to and
**n**doubles and**h**halves each go, error should go down by each iteration and convergence is fast. So, in practice, one halves**h**until change in integral between steps is less than some assigned value.

Geoffrey Fox, Northeast Parallel Architectures Center at Syracuse University, gcf@npac.syr.edu