Four-Point Optimal Sixteenth-Order Iterative Method for Solving Nonlinear Equations

Table 2

Numerical comparison of absolute error |𝑥_𝑛−𝛼|, number of iterations = 3.

(𝑓𝑛(𝑥),𝑥0)	Iter/COC	MA	BT	GK1	GK2
𝑓1, 1.0	1	0.00268	0.00183	0.0111	0.00230
	2	2.03𝑒−37	1.71𝑒−37	6.35𝑒−24	5.61𝑒−34
	3	𝟐.𝟒𝟕𝐞−𝟓𝟖𝟑	3.53𝑒−582	1.37𝑒−363	1.03𝑒−523
	COC	16	16	16	16
𝑓2, 2.5	1	0.04086	0.0639	0.0296	0.00866
	2	6.16𝑒−9	650.0	5.35𝑒−14	2.53𝑒−21
	3	1.50𝑒−121	Divergent	4.79𝑒−201	𝟏.𝟖𝟗𝐞−𝟑𝟏𝟕
	COC	16.5	—	15.9	16.0
𝑓3, 2.5	1	0.0000326	0.0000303	0.000497	0.0000677
	2	4.87𝑒−73	1.70𝑒−72	1.56𝑒−51	1.14𝑒−64
	3	𝟑.𝟏𝟏𝐞−𝟏𝟏𝟓𝟖	1.63𝑒−1148	1.42𝑒−811	4.52𝑒−1021
	COC	16	16	16	16
𝑓4, 1/6	1	2.79𝑒−7	0.0000864	1.28𝑒−7	0.000167
	2	1.00𝑒−109	1.18𝑒−63	2.28𝑒−107	9.28𝑒−57
	3	𝟐.𝟖𝟎𝐞−𝟏𝟖𝟓𝟏	1.72𝑒−1005	2.24𝑒−1703	7.82𝑒−893
	COC	17	16	16	16
𝑓5, 3.0	1	0.0486	0.135	0.0949	0.0133
	2	1.95𝑒−22	1.81𝑒−17	1.78𝑒−19	1.11𝑒−35
	3	8.46𝑒−349	1.79𝑒−271	6.86𝑒−302	𝟐.𝟔𝟏𝐞−𝟓𝟔𝟑
	COC	16.0	16.0	15.9	16.0