New Derivative Based Open Newton-Cotes Quadrature Rules

Table 20

Results and observed orders for the rules with order 10, for ∫¹₀(𝑥ln(1+𝑥)/(1+𝑥²))𝑑𝑥.

𝑁	1	2	4	8	16
Nine point ONC	1.295725718	1.143369947	1.097799574	1.075658649	1.064314363
𝑝	NA	0.20	0.07	0.03	0.02
Five point ONC1	0.162863548	0.162865010	0.162865006	0.162865006	0.162865006
𝑝	NA	NA	Exact	Exact	Exact
Four point ONC2	0.1628657293	0.1628650035	0.1628650059	0.1628650059	0.1628650059
𝑝	NA	NA	Exact	Exact	Exact