New Derivative Based Open Newton-Cotes Quadrature Rules

Table 18

Results and observed orders for the rules with order 8, for ∫²₀𝑒^−𝑥2𝑑𝑥.

𝑁	1	2	4	8	16
Seven point ONC	0.882649378	0.882081616	0.882081390	0.882081396	0.882081393
𝑝	NA	NA	NA	NA	1.39
Four point ONC1	0.882908200	0.882081724	0.882081389	0.882081391	0.882081391
𝑝	NA	11.31	NA	Exact	Exact
Three point ONC2	0.881359024	0.882081118	0.882081391	0.882081391	0.882081391
𝑝	NA	11.33	11.37	Exact	Exact
Five point ONC3	0.882611232	0.882081598	0.882081390	0.882081390	0.882081392
𝑝	NA	11.62	8.42	Exact	Exact
Five point ONC4	0.881613287	0.882081217	0.882081391	0.882081391	0.882081391
𝑝	NA	11.32	Exact	Exact	Exact