On Some Iterative Methods with Memory and High Efficiency Index for Solving Nonlinear Equations

Table 2

Families of three-point methods with memory, for example, 𝑓₂(𝑥).

Methods	|𝑥1−𝛼|	|𝑥2−𝛼|	|𝑥3−𝛼|	𝑟𝑐
𝜙1
(12), (6)	0.104𝑒−3	0.127𝑒−39	0.868𝑒−425	10.725
(12), (7)	0.104𝑒−3	0.116𝑒−39	0.419𝑒−436	11.027
(12), (8)	0.104𝑒−3	0.261𝑒−40	0.259𝑒−443	11.010
𝜙2
(12), (6)	0.106𝑒−3	0.499𝑒−36	0.142𝑒−360	10.040
(12), (7)	0.106𝑒−3	0.476𝑒−36	0.507𝑒−360	10.016
(12), (8)	0.106𝑒−3	0.223𝑒−36	0.254𝑒−363	10.005
𝜙3
(12), (6)	0.104𝑒−3	0.127𝑒−39	0.868𝑒−425	10.725
(12), (7)	0.104𝑒−3	0.116𝑒−39	0.419𝑒−436	11.027
(12), (8)	0.104𝑒−3	0.261𝑒−40	0.259𝑒−443	11.010