A Family of Fourteenth-Order Convergent Iterative Methods for Solving Nonlinear Equations

Table 2

Numerical comparisons.

𝑓(𝑥)		NM	BI	SP	SS	M1	M2
𝑓1(𝑥), 𝑥0=4.9	𝑛	8	499	2	499	3	2
	nfe	16	—	10	—	15	10
	COC	1.99	—	10.80	—	11.89	11.68
	𝑓(𝑥𝑛)	0.12710^−18	𝐷	0.12710^−17	𝐷	0.19710^−24	0.62310^−50
𝑓2(𝑥),𝑥0=9.9	𝑛	7	3	2	2	2	2
	nfe	14	12	10	10	10	10
	COC	2.00	8.33	11.83	13.02	12.05	12.11
	𝑓(𝑥𝑛)	0.759 10^−20	0.11610^−51	0.22110^−26	0.12410^−27	0.51610^−30	0.29710^−31
𝑓3(𝑥),𝑥0=8.0	𝑛	8	9	2	3	3	2
	nfe	16	36	10	15	15	10
	COC	1.99	7.72	11.21	14.81	13.50	12.01
	𝑓(𝑥𝑛)	0.24510^−19	0.11610^−41	0.28710^−18	0.64110^−62	0.31810^−87	0.48110^−63
𝑓4(𝑥),𝑥0=9.8	𝑛	7	3	2	2	2	2
	nfe	14	12	10	10	10	10
	COC	1.99	8.00	13.30	14.07	13.02	13.03
	𝑓(𝑥𝑛)	0.16510^−19	0.55510^−114	0.30410^−37	0.47510^−54	0.54310^−50	0.22510^−32
𝑓5(𝑥),𝑥0=15.5	𝑛	5	2	2	2	2	2
	nfe	10	8	10	10	10	10
	COC	2.00	7.82	13.90	14.84	13.87	13.88
	𝑓(𝑥𝑛)	0.11910^−24	0.75110^−49	0.15510^−170	0.51210^−165	0.27910^−142	0.58410^−151
𝑓6(𝑥),𝑥0=7.7	𝑛	7	3	3	2	2	2
	nfe	14	12	15	10	10	10
	COC	1.99	7.96	13.94	11.64	10.76	13.91
	𝑓(𝑥𝑛)	0.48610^−22	0.94110^−45	0.53810^−63	0.22910^−23	0.14010^−21	0.57010^−20
𝑓7(𝑥),𝑥0=11.9	𝑛	5	2	2	2	2	2
	nfe	10	8	10	10	10	10
	COC	2.00	7.89	13.91	14.91	14.07	14.05
	𝑓(𝑥𝑛)	0.31110^−26	0.18510^−49	0.64910^−176	0.47410^−174	0.44910^−166	0.26110^−179
𝑓8(𝑥),𝑥0=1.6	𝑛	5	2	2	2	2	2
	nfe	10	8	10	10	10	10
	COC	1.99	7.86	13.96	14.94	13.91	13.93
	𝑓(𝑥𝑛)	0.35410^−18	0.40210^−36	0.21310^−137	0.35910^−144	0.12810^−127	0.23310^−128
𝑓9(𝑥),𝑥0=−0.5	𝑛	6	2	2	2	2	2
	nfe	12	8	10	10	10	10
	COC	1.99	7.45	13.76	14.69	13.50	13.54
	𝑓(𝑥𝑛)	0.10310^−25	0.51410^−27	0.14910^−80	0.29010^−100	0.48610^−117	0.23110^−97
𝑓10(𝑥),𝑥0=1.0	𝑛	5	2	2	2	2	2
	nfe	10	8	10	10	10	10
	COC	2.00	8.32	14.17	15.25	14.19	14.17
	𝑓(𝑥𝑛)	0.26510^−26	0.16410^−43	0.15210^−136	0.51810^−148	0.18810^−132	0.86410^−138
𝑓11(𝑥),𝑥0=1.8	𝑛	5	2	2	2	2	2
	nfe	10	8	10	10	10	10
	COC	1.99	8.19	14.02	15.08	14.17	14.08
	𝑓(𝑥𝑛)	0.59310^−28	0.50310^−55	0.60010^−179	0.95210^−223	0.13810^−198	0.94610^−184
𝑓12(𝑥),𝑥0=3.5	𝑛	6	3	2	2	2	2
	nfe	12	12	10	10	10	10
	COC	1.99	7.99	12.44	13.69	12.92	12.52
	𝑓(𝑥𝑛)	0.98010^−21	0.22710^−124	0.98510^−58	0.18610^−62	0.18610^−53	0.12210^−51
𝑓13(𝑥),𝑥0=−1.5	𝑛	4	2	2	2	2	2
	nfe	8	8	10	10	10	10
	COC	1.99	7.84	13.78	14.87	13.87	13.89
	𝑓(𝑥𝑛)	0.31510^−17	0.68210^−43	0.17110^−126	0.40610^−149	0.34310^−136	0.19210^−133
𝑓14(𝑥),𝑥0=25.0	𝑛	12	499	3	6	4	3
	nfe	24	—	15	30	20	15
	COC	1.99	—	12.81	14.14	11.10	13.31
	𝑓(𝑥𝑛)	0.38210^−32	𝐷	0.11510^−28	0.12310^−44	0.10110^−16	0.53910^−75
𝑓15(𝑥),𝑥0=2.1	𝑛	4	2	2	2	2	2
	nfe	8	8	10	10	10	10
	COC	1.99	8.30	14.33	15.28	14.26	14.28
	𝑓(𝑥𝑛)	0.54710^−21	0.23710^−55	0.27210^−160	0.11910^−203	0.15510^−164	0.18510^−79