New Derivative Based Open Newton-Cotes Quadrature Rules

Table 22

Results and observed orders for the rules with order 10, for ∫³₀𝑒^−2𝑥sin(4𝑥)𝑑𝑥.

𝑁	1	2	4	8	16
Nine point ONC	0.526431102	−0.041135432	1.51645849	1.38389260	1.31653544
𝑝	NA	NA	NA	0.15	0.08
Five point ONC1	0.152040549	0.199941942	0.199714629	0.199714662	0.199714662
𝑝	NA	NA	NA	Exact	Exact
Four point ONC2	0.219131222	0.199573932	0.199714685	0.199714662	0.199714662
𝑝	NA	NA	7.36	Exact	Exact