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

Table 6

Comparison of the norm of the error occurring in the estimates of the exact root with some existing fourth-order methods.

Example	Method	‖𝑋1^(𝑘)−𝛼‖	‖𝑋2^(𝑘)−𝛼‖	‖𝑋3^(𝑘)−𝛼‖
Example 1	M4 II	6.0516𝑒−7	5.2164𝑒−28	4.1540𝑒−112
	BBK	1.5583𝑒−6	6.4678𝑒−26	2.6115𝑒−103
	JR	9.5374𝑒−7	5.3169𝑒−27	7.1439𝑒−108
	MT	9.3744𝑒−7	5.2761𝑒−27	6.9541𝑒−108
Example 2	M4 II	1.088𝑒−1	3.4338𝑒−6	3.0799𝑒−24
	BBK	9.4638𝑒−2	9.2598𝑒−6	8.3045𝑒−22
	JR	9.8464𝑒−2	5.4080𝑒−6	4.6299𝑒−23
	MT	2.5630𝑒−2	1.0710𝑒−8	8.4788𝑒−34
Example 3	M4 II	2.0890𝑒−4	1.1590𝑒−16	4.0534𝑒−67
	BBK	5.1609𝑒−4	9.7061𝑒−15	4.4270𝑒−59
	JR	3.0309𝑒−4	7.5797𝑒−16	1.0992𝑒−63
	MT	2.6127𝑒−4	3.5709𝑒−16	4.6078𝑒−65
Example 4	M4 II	1.0527𝑒−2	4.6896𝑒−8	1.6605𝑒−29
	BBK	3.5372𝑒−2	9.9178𝑒−6	1.0195𝑒−19
	JR	2.4911𝑒−2	1.5682𝑒−6	3.3904𝑒−23
	MT	3.0081𝑒−2	3.5059𝑒−6	1.1628𝑒−21
Example 5	M4 II	1.6108𝑒−6	8.8401𝑒−24	6.5622𝑒−93
	BBK	5.3003𝑒−6	2.7113𝑒−21	1.4597𝑒−82
	JR	2.8482𝑒−6	1.3655𝑒−22	5.7544𝑒−88
	MT	3.4874𝑒−6	3.0141𝑒−22	1.2962𝑒−86
Example 6	M4 II	1.7279𝑒−4	4.5090𝑒−17	2.0519𝑒−69
	BBK	4.0878𝑒−4	3.2118𝑒−15	1.2129𝑒−59
	JR	2.4748𝑒−4	2.7691𝑒−16	4.2681𝑒−64
	MT	2.0133𝑒−4	1.0206𝑒−16	6.7467𝑒−66