New Eighth-Order Derivative-Free Methods for Solving Nonlinear Equations

Table 3

Errors occurring in the estimates of the root of (4.3) by the methods described.

Methods	|𝑥1−𝛼|	|𝑥2−𝛼|	|𝑥3−𝛼|	COC
(2.7)	0.241𝑒−4	0.872𝑒−37	0.258𝑒−296	7.9859
(3.3)	0.813𝑒−2	0.152𝑒−17	0.264𝑒−143	7.9961
(3.5)	0.416	0.370	0.661𝑒−4	0.8817
(3.7)	0.750𝑒−2	0.599𝑒−18	0.110𝑒−146	8.0254
(3.9)	0.128𝑒−2	0.355𝑒−24	0.123𝑒−196	8.0317
(3.11)	0.153𝑒−2	0.101𝑒−22	0.367𝑒−184	7.9999
(3.13)	0.205𝑒−2	0.104𝑒−21	0.447𝑒−176	7.9998
(3.15)	0.178𝑒−2	0.332𝑒−22	0.502𝑒−180	7.9998
(3.17)	−−	−−	−−	−−