A New Optimal Eighth-Order Ostrowski-Type Family of Iterative Methods for Solving Nonlinear Equations

Table 2

Comparison of various iterative methods under the same total number of function evaluations (TNFE = 12).

	(21)	(24)	(27)	(BM)	(LWM)	(ShM)
𝑓1,𝑥0=0
|𝑥𝑛−𝛼|	0.23𝑒−643	0.18𝑒−654	0.42𝑒−662	0.46𝑒−650	0.24𝑒−613	0.90𝑒−656
|𝑓(𝑥𝑛)|	0.85𝑒−643	0.68𝑒−654	0.16𝑒−661	0.17𝑒−649	0.91𝑒−613	0.34𝑒−655
COC	8.000000	8.000000	8.000000	8.000000	8.000000	8.000000
𝑓2,𝑥0=−1
|𝑥𝑛−𝛼|	0.24𝑒−307	0.39𝑒−293	0.26𝑒−297	0.48𝑒−217	0.14𝑒−340	0.65𝑒−430
|𝑓(𝑥𝑛)|	0.49𝑒−306	0.79𝑒−292	0.53𝑒−296	0.97𝑒−216	0.28𝑒−339	0.13𝑒−428
COC	8.000001	8.000002	8.000002	7.999999	8.000000	8.000000
𝑓3,𝑥0=2
|𝑥𝑛−𝛼|	0.32𝑒−83	0.610𝑒−92	0.74𝑒−77	0.10𝑒−107	0.79𝑒−52	0.14𝑒−96
|𝑓(𝑥𝑛)|	0.32𝑒−83	0.610𝑒−92	0.74𝑒−77	0.10𝑒−107	0.79𝑒−52	0.14𝑒−96
COC	7.986895	7.993900	7.984913	7.965999	7.899280	7.991216
𝑓4,𝑥0=1.6
|𝑥𝑛−𝛼|	0.12𝑒−368	0.11𝑒−359	0.21𝑒−361	0.66𝑒−303	0.97𝑒−307	0.51𝑒−341
|𝑓(𝑥𝑛)|	0.45𝑒−367	0.41𝑒−358	0.78𝑒−360	0.24𝑒−301	0.36𝑒−305	0.19𝑒−339
COC	7.999999	7.999997	8.000018	7.999999	7.999999	8.000000
𝑓5,𝑥0=1.8
|𝑥𝑛−𝛼|	0.15𝑒−472	0.13𝑒−471	0.10𝑒−485	0.26𝑒−446	0.47𝑒−399	0.17𝑒−444
|𝑓(𝑥𝑛)|	0.42𝑒−472	0.36𝑒−471	0.28𝑒−485	0.72𝑒−446	0.13𝑒−398	0.46𝑒−444
COC	8.000000	8.000000	8.000000	8.000000	8.000000	8.000000
𝑓6,𝑥0=1
|𝑥𝑛−𝛼|	0.11𝑒−632	0.33𝑒−572	0.99𝑒−558	0.98𝑒−664	0.49𝑒−581	0.71𝑒−570
|𝑓(𝑥𝑛)|	0.18𝑒−632	0.56𝑒−572	0.17𝑒−557	0.16𝑒−663	0.81𝑒−581	0.12𝑒−569
COC	8.000000	8.000000	8.000000	8.000000	8.000000	8.000000
𝑓7,𝑥0=−0.5
|𝑥𝑛−𝛼|	0.27𝑒−235	0.17𝑒−198	0.84𝑒−192	0.31𝑒−221	0.13𝑒−221	0.35𝑒−193
|𝑓(𝑥𝑛)|	0.80𝑒−235	0.52𝑒−198	0.25𝑒−191	0.94𝑒−221	0.39𝑒−221	0.11𝑒−192
COC	8.015338	8.000253	8.000189	8.000058	8.000030	7.999924
𝑓8,𝑥0=3.2
|𝑥𝑛−𝛼|	0.31𝑒−518	0.10𝑒−485	0.12𝑒−476	0.19𝑒−618	0.58𝑒−487	0.26𝑒−479
|𝑓(𝑥𝑛)|	0.19𝑒−518	0.62𝑒−486	0.69𝑒−477	0.11𝑒−618	0.35𝑒−487	0.16𝑒−479
COC	8.000000	8.000000	8.000000	8.000000	8.000000	8.000000