New Derivative Based Open Newton-Cotes Quadrature Rules

Table 19

Results and observed orders for the rules with order 8, for ∫³₀𝑒^−2𝑥sin(4𝑥)𝑑𝑥.

𝑁	1	2	4	8	16
Seven point ONC	0.116217345	0.199107249	0.199722936	0.199714694	0.199714661
𝑝	NA	7.10	NA	8.02	7.98
Four point ONC1	0.086930244	0.198791095	0.199726603	0.199714706	0.199714662
𝑝	NA	6.93	NA	8.07	Exact
Three point ONC2	0.345139247	0.200290872	0.199703568	0.199714621	0.199714662
𝑝	NA	7.97	7.94	8.08	Exact
Five point ONC3	0.114010828	0.199174615	0.199722444	0.199714691	0.199714662
𝑝	NA	NA	5.72	6.49	Exact
Five point ONC4	0.297964032	0.200061133	0.199707419	0.199714636	0.199714662
𝑝	NA	8.14	NA	8.11	Exact