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

Table 3

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

Function	Guess	Method	|𝑥1−𝛼|	|𝑥2−𝛼|	|𝑥3−𝛼|
𝑓1	5	SL4	0.14780𝑒−5	0.47702𝑒−23	0.51761𝑒−93
		KH4	0.47426𝑒−9	0.16796𝑒−40	0.26418𝑒−166
		M4 I	0.42743𝑒−9	0.99425𝑒−41	0.29108𝑒−167
		M4 II	0.41059𝑒−9	0.81178𝑒−41	0.12404𝑒−167
𝑓2	2.5	SL4	0.26594𝑒−1	0.32982𝑒−6	0.76311𝑒−26
		KH4	0.14965𝑒−1	0.45484𝑒−7	0.40826𝑒−29
		M4 I	0.76770𝑒−2	0.12105𝑒−8	0.76261𝑒−36
		M4 II	0.36004𝑒−2	0.23379𝑒−10	0.41876𝑒−43
𝑓3	0.4	SL4	0.86290𝑒−7	0.78612𝑒−28	0.54150𝑒−112
		KH4	0.52074𝑒−7	0.67319𝑒−29	0.18803𝑒−116
		M4 I	0.24363𝑒−7	0.14724𝑒−30	0.19642𝑒−123
		M4 II	0.14232𝑒−7	0.98181𝑒−32	0.22236𝑒−128
𝑓4	0.3	SL4	0.14507𝑒−1	0.20259𝑒−6	0.81662𝑒−26
		KH4	0.56586𝑒−1	0.78841𝑒−4	0.41658𝑒−15
		M4 I	0.11886𝑒−1	0.73037𝑒−7	0.10950𝑒−27
		M4 II	0.40617𝑒−2	0.36373𝑒−9	0.23749𝑒−37