New Derivative Based Open Newton-Cotes Quadrature Rules

Table 12

Results and observed orders for the rules with order 4, for ∫²₀𝑒^−𝑥2𝑑𝑥.

𝑁	1	2	4	8	16
Three point ONC	0.933680383	0.882318596	0.882095283	0.882082261	0.882081446
𝑝	NA	7.76	8.10	4.21	NA
Four point ONC	0.915679501	0.882245499	0.882091045	0.882081995	0.882081429
𝑝	NA	7.67	8.10	4.31	NA
Two point ONC1	0.944928707	0.882363060	0.882097854	0.882082422	0.882081455
𝑝	NA	7.80	4.09	4.01	4.19
One point ONC2	0.723548456	0.881147401	0.882025799	0.882077911	0.882081173
𝑝	NA	7.41	4.07	3.99	3.95
Two point ONC3	0.944928707	0.882363060	0.882097854	0.882082422	0.882081455
𝑝	NA	7.80	4.09	4.01	4.19
One point ONC4	0.723548456	0.881147401	0.882025799	0.882077911	0.882081173
𝑝	NA	7.41	4.07	3.99	3.95
Two point ONC4	0.802053420	0.881569701	0.882050796	0.882079476	0.882081271
𝑝	NA	7.29	4.06	3.99	3.91