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

Table 1

Families of three-point methods with memory, for example, 𝑓₁(𝑥).

Methods	|𝑥1−𝛼|	|𝑥2−𝛼|	|𝑥3−𝛼|	𝑟𝑐
𝜙1
(12), (6)	0.665𝑒−4	0.186𝑒−43	0.374𝑒−468	10.737
(12), (7)	0.665𝑒−4	0.718𝑒−44	0.592𝑒−484	11.011
(12), (8)	0.665𝑒−4	0.471𝑒−44	0.321𝑒−487	11.038
𝜙2
(12), (6)	0.665𝑒−4	0.468𝑒−40	0.800𝑒−402	10.007
(12), (7)	0.665𝑒−4	0.231𝑒−40	0.996𝑒−406	10.021
(12), (8)	0.665𝑒−4	0.276𝑒−40	0.579𝑒−405	10.023
𝜙3
(12), (6)	0.665𝑒−4	0.186𝑒−43	0.374𝑒−468	10.737
(12), (7)	0.665𝑒−4	0.718𝑒−44	0.592𝑒−484	11.011
(12), (8)	0.665𝑒−4	0.471𝑒−44	0.321𝑒−487	11.038