Some Class of Third- and Fourth-Order Iterative Methods for Solving Nonlinear Equations

Table 2

Comparison of the absolute error occurring in the estimates of the exact root.

Function	Guess	Method	|𝑥1−𝛼|	|𝑥2−𝛼|	|𝑥3−𝛼|
𝑓1	5	NM	0.21464𝑒−4	0.83264𝑒−11	0.12530𝑒−23
		WR3	0.11208𝑒−6	0.37810𝑒−23	0.14517𝑒−72
		HM3	0.12544𝑒−6	0.59456𝑒−23	0.63310𝑒−72
		CH3	0.98734𝑒−7	0.22705𝑒−23	0.27611𝑒−73
		M3	0.13882𝑒−6	0.89316𝑒−23	0.23790𝑒−71
𝑓2	2.5	NM	0.85925𝑒−1	0.32675𝑒−2	0.50032𝑒−5
		WR3	0.18271𝑒−1	0.14770𝑒−5	0.79610𝑒−18
		HM3	0.49772𝑒−2	0.33027𝑒−8	0.95318𝑒−27
		CH3	0.27815𝑒−1	0.95903𝑒−5	0.41254𝑒−15
		M3	0.14819𝑒−1	0.64153𝑒−6	0.51267𝑒−19
𝑓3	0.4	NM	0.10737𝑒−3	0.50901𝑒−8	0.11442𝑒−16
		WR3	0.20631𝑒−6	0.53436𝑒−21	0.92858𝑒−65
		HM3	0.52795𝑒−6	0.19743𝑒−19	0.10325𝑒−59
		CH3	0.93064𝑒−6	0.20624𝑒−18	0.22446𝑒−56
		M3	0.12723𝑒−5	0.67803𝑒−18	0.10261𝑒−54
𝑓4	0.3	NM	0.47567𝑒−1	0.22849𝑒−2	0.55356𝑒−5
		WR3	0.13039𝑒−1	0.31800𝑒−5	0.45048𝑒−16
		HM3	0.64393𝑒−3	0.72236𝑒−10	0.10226𝑒−30
		CH3	0.34012𝑒−1	0.11125𝑒−3	0.34855𝑒−11
		M3	0.75418𝑒−2	0.36460𝑒−6	0.41629𝑒−19