NI.1: Newton-Cotes Formulae

• (i) We write

  

  where is assumed known at and is sufficiently simple so that integrals (NI.3), involving it, can be calculated. Of course, we split off to make smoother and more reasonably approximated as a polynomial.

• We assume the form:

  

  where the n+1 's are to be found by requiring I to be exact for all polynomials of degree .

• This is easy-for put

  

  which are calculable constants.

  

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