Some New Iterative Methods for Nonlinear Equations

Table 1

Numerical examples.

	IT	𝑥𝑛	𝑓(𝑥𝑛)	𝛿	𝑝
𝑓1,𝑥0=−1
NM	7	1.40449164821534122603508681779	−1.04𝑒−50	7.33𝑒−26	2.00003
NNT	5	1.40449164821534122603508681779	0	4.86𝑒−29	3.16501
CM	5	1.40449164821534122603508681779	0	1.31𝑒−17	2.85844
NR1	5	1.40449164821534122603508681779	0	3.19𝑒−32	3.03300
NR2	4	1.40449164821534122603508681779	0	1.50𝑒−25	4.31447
𝑓2,𝑥0=2
NM	6	0.25753028543986076045536730494	2.93𝑒−55	9.10𝑒−28	2.00050
NNT	5	0.25753028543986076045536730494	1.00𝑒−59	1.77𝑒−24	2.82952
CM	4	0.25753028543986076045536730494	0	9.46𝑒−29	4.57143
NR1	4	0.25753028543986076045536730494	−3.70𝑒−52	2.24𝑒−17	3.57234
NR2	4	0.25753028543986076045536730494	−1.00𝑒−59	3.55𝑒−43	4.25114
𝑓3,𝑥0=3.5
NM	8	2	2.06𝑒−42	8.28𝑒−22	2.00025
NNT	5	2	0	3.45𝑒−24	2.83484
CM	5	2	0	2.74𝑒−24	3.53144
NR1	6	2	0	1.66𝑒−40	2.99063
NR2	5	2	0	2.14𝑒−42	3.86697
𝑓4,𝑥0=1.5
NM	7	2.15443469003188372175929356652	2.06𝑒−54	5.64𝑒−28	2.00003
NNT	5	2.15443469003188372175929356652	1.00𝑒−58	4.70𝑒−43	2.65300
CM	5	2.15443469003188372175929356652	1.00𝑒−58	1.57𝑒−22	3.48932
NR1	5	2.15443469003188372175929356652	−8.00𝑒−59	1.45𝑒−35	3.01710
NR2	4	2.15443469003188372175929356652	−8.00𝑒−59	3.79𝑒−28	4.20825
𝑓_5,𝑥_0=−2
NM	9	−1.20764782713091892700941675836	−2.27𝑒−40	2.73𝑒−21	2.00085
NNT	5	−1.20764782713091892700941675836	8.00𝑒−59	1.53𝑒−32	2.22201
CM	6	−1.20764782713091892700941675836	−1.10𝑒−58	2.15𝑒−36	3.88967
NR1	6	−1.20764782713091892700941675836	−2.65𝑒−56	8.33𝑒−20	3.01400
NR2	5	−1.20764782713091892700941675836	−1.10𝑒−58	2.34𝑒−20	4.04259
𝑓_6,𝑥_0=3.5
NM	13	3	1.52𝑒−47	4.21𝑒−25	2.00023
NNT	7	3	0	1.65𝑒−30	2.38562
CM	8	3	0	2.12𝑒−23	3.68024
NR1	9	3	0	1.24𝑒−37	2.99410
NR2	7	3	0	4.33𝑒−23	3.84449