Eighth-Order Iterative Methods without Derivatives for Solving Nonlinear Equations

Table 2

Comparison of various iterative methods.

Functions	K-T	Liu1	Liu2	RT	SKK
𝑓1(𝑥),𝑥0=1.9	0.199𝑒−37	0.121𝑒−66	0.108𝑒−66	0.114𝑒−75	—
𝑓2(𝑥),𝑥0=−1.5	0.166𝑒−158	0.832𝑒−207	0.490𝑒−282	0.128𝑒−156	0.145𝑒−100
𝑓3(𝑥),𝑥0=1.6	0.172𝑒−258	0.629𝑒−417	0.204𝑒−393	0.498𝑒−297	0.308𝑒−285
𝑓4(𝑥),𝑥0=0.125	0.166𝑒−1385	0.107𝑒−1133	0.868𝑒−800	0.566𝑒−1060	0.609𝑒−220
𝑓5(𝑥),𝑥0=4.4	0.115𝑒−927	0.350𝑒−1017	0.268𝑒−1022	0.471𝑒−1025	0.639𝑒−791
𝑓6(𝑥),𝑥0=3.1	0.118𝑒−32	0.581𝑒−59	0.236𝑒−58	0.224𝑒−53	0.191𝑒−12
𝑓7(𝑥),𝑥0=0.75	0.756𝑒−568	0.119𝑒−571	0.333𝑒−607	0.522𝑒−557	0.367𝑒−335
𝑓8(𝑥),𝑥0=0.5	0.260𝑒−317	0.651𝑒−344	0.205𝑒−301	0.298𝑒−285	0.253𝑒−685
𝑓9(𝑥),𝑥0=0.5	0.293𝑒−416	0.713𝑒−433	0.347𝑒−448	0.644𝑒−423	0.535𝑒−283
𝑓10(𝑥),𝑥0=2.5	0.687𝑒−739	0.439𝑒−696	0.981𝑒−698	0.121𝑒−694	0.770𝑒−643