New Derivative Based Open Newton-Cotes Quadrature Rules

Table 13

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

𝑁	1	2	4	8	16
Three point ONC	0.086043984	0.367562601	0.201398942	0.199657135	0.199709254
𝑝	NA	NA	6.64	NA	3.41
Four point ONC	0.269179529	0.310254438	0.200767736	0.199673399	0.199710886
𝑝	NA	0.67	6.71	NA	3.44
Two point ONC1	−0.04987788	0.403160349	0.201798239	0.199647441	0.199708266
𝑝	NA	NA	6.61	NA	3.93
One point ONC2	−1.53759876	−0.31986670	0.195705275	0.199975525	0.199736732
𝑝	NA	1.74	7.02	NA	3.56
Two point ONC3	−0.04987788	0.403160349	0.201798239	0.199647441	0.199708266
𝑝	NA	NA	6.61	NA	3.93
One point ONC4	−1.53759876	−0.31986670	0.195705275	0.199975525	0.199736732
𝑝	NA	1.74	7.02	NA	3.56
Two point ONC4	−1.12369531	−0.06440215	0.197908079	0.199862681	0.199726870
𝑝	NA	2.32	7.19	NA	3.59