A New Sixth-Order Steffensen-Type Iterative Method for Solving Nonlinear Equations

Table 2

Comparison of various iterative methods.

	New method	(CM)	(SHM)	(YIM)	(SM)
𝑓1,𝑥0=0
𝑥𝑛−𝛼	0.23𝑒−291	0.46𝑒−165	0.36𝑒−267	0.45𝑒−155	0.55𝑒−80
𝑓𝑥𝑛	0.88𝑒−291	0.18𝑒−164	0.14𝑒−266	0.17𝑒−154	0.21𝑒−79
COC	6.000000	6.000006	6.000000	5.999992	2.000000
TNFE	12	15	12	12	12
𝑓2,𝑥0=−1.2
𝑥𝑛−𝛼	0.36𝑒−345	0.34𝑒−180	0.12𝑒−157	0.67𝑒−190	0.32𝑒−40
𝑓𝑥𝑛	0.73𝑒−344	0.69𝑒−179	0.24𝑒−156	0.14𝑒−188	0.65𝑒−39
COC	6.000000	5.999994	6.000004	6.000000	2.000000
TNFE	12	15	12	12	12
𝑓3,𝑥0=0.1
𝑥𝑛−𝛼	0.43𝑒−145	0.41𝑒−158	0.52𝑒−121	0.13𝑒−88	0.71𝑒−32
𝑓𝑥𝑛	0.43𝑒−145	0.41𝑒−158	0.52𝑒−121	0.13𝑒−88	0.71𝑒−32
COC	5.999990	5.999996	5.999862	5.999567	2.000000
TNFE	12	15	12	12	12
𝑓4,𝑥0=1.8
𝑥𝑛−𝛼	0.13𝑒−188	0.12𝑒−280	0.99𝑒−171	0.43𝑒−93	0.38𝑒−48
𝑓𝑥𝑛	0.35𝑒−188	0.35𝑒−280	0.27𝑒−170	0.12𝑒−92	0.11𝑒−47
COC	6.000000	6.000000	5.999998	5.999951	2.000000
TNFE	12	15	12	12	12
𝑓5,𝑥0=1
𝑥𝑛−𝛼	0.21𝑒−265	0.14𝑒−204	0.31𝑒−257	0.14𝑒−133	0.54𝑒−88
𝑓𝑥𝑛	0.36𝑒−265	0.24𝑒−204	0.515𝑒−257	0.23𝑒−133	0.91𝑒−88
COC	6.000000	6.000000	6.000000	6.000024	2.000000
TNFE	12	15	12	12	12
𝑓6,𝑥0=−0.75
𝑥𝑛−𝛼	0.48𝑒−109	0.11𝑒−104	0.87𝑒−74	0.18𝑒−22	0.11𝑒−12
𝑓𝑥𝑛	0.15𝑒−108	0.34𝑒−104	0.26𝑒−73	0.54𝑒−22	0.34𝑒−12
COC	5.999904	5.999991	5.996977	5.920939	1.999927
TNFE	12	15	12	12	12
𝑓7,𝑥0=3.2
𝑥𝑛−𝛼	0.14𝑒−265	0.41𝑒−199	0.61𝑒−316	0.12𝑒−168	0.21𝑒−98
𝑓𝑥𝑛	0.84𝑒−266	0.24𝑒−199	0.37𝑒−316	0.72𝑒−169	0.13𝑒−98
COC	6.000000	6.000000	6.000000	6.000001	2.000000
TNFE	12	15	12	12	12