New Derivative Based Open Newton-Cotes Quadrature Rules

Table 16

Results and observed orders for the rules with order 6, for ∫³₀𝑒^−2𝑥sin(4𝑥)𝑑𝑥.

𝑁	1	2	4	8	16
Five point ONC	0.668675155	0.180576440	0.199344558	0.199710595	0.199714605
𝑝	NA	NA	5.69	6.50	6.15
Six point ONC	0.506621196	0.186032806	0.199455606	0.199711798	0.199714622
𝑝	NA	NA	5.72	6.50	6.17
Three point ONC1	0.848922696	0.174588551	0.199223240	0.199709279	0.199714586
𝑝	NA	NA	5.67	6.51	6.14
Two point ONC2	−0.425713982	0.239513474	0.200436683	0.199722775	0.199714778
𝑝	NA	NA	5.78	6.47	6.13
Three point ONC3	0.848922696	0.174588551	0.199223240	0.199709279	0.199714586
𝑝	NA	NA	5.67	6.51	6.14
Four point ONC3	0.548955957	0.184222649	0.199422043	0.199714258	0.199714616
𝑝	NA	NA	5.72	9.49	6.13
Three point ONC4	−0.023868456	0.230076741	0.200260208	0.199720813	0.199714749
𝑝	NA	NA	5.79	6.47	6.15
Four point ONC4	−0.02248199	0.218175909	0.200040826	0.199718362	0.199714715
𝑝	NA	NA	5.82	6.46	6.13