New Derivative Based Open Newton-Cotes Quadrature Rules

Table 21

Results and observed orders for the rules with order 10, for ∫²₀𝑒^−𝑥2𝑑𝑥.

𝑁	1	2	4	8	16
Nine point ONC	3.470923242	5.116115937	5.430111149	5.567289203	5.634338380
𝑝	NA	−0.71	−0.10	−0.04	−0.02
Five point ONC1	0.882047084	0.882081362	0.882081390	0.882081389	0.882081391
𝑝	NA	9.85	2.07	0.41	Exact
Four point ONC2	0.882104655	0.882081409	0.882081391	0.882081391	0.882081391
𝑝	NA	11.12	Exact	Exact	Exact