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International Scholarly Research Notices
Table of Contents
International Scholarly Research Notices
/
2011
/
Article
/
Tab 1
/
Research Article
Eighth-Order Iterative Methods without Derivatives for Solving Nonlinear Equations
Table 1
Test functions and their roots.
Function
Root
𝑓
1
(
𝑥
)
=
(
𝑥
−
2
)
(
𝑥
1
0
+
𝑥
+
1
)
e
x
p
(
−
𝑥
−
1
)
,
𝛼
=
2
𝑓
2
(
𝑥
)
=
e
x
p
(
−
𝑥
2
+
𝑥
+
2
)
−
c
o
s
(
𝑥
+
1
)
+
𝑥
3
+
1
,
𝛼
=
−
1
𝑓
3
(
𝑥
)
=
s
i
n
(
𝑥
)
2
−
𝑥
2
+
1
,
𝛼
=
1
.
4
0
4
4
9
1
6
5
⋯
𝑓
4
(
𝑥
)
=
𝑒
−
𝑥
−
c
o
s
(
𝑥
)
,
𝛼
=
−
0
.
6
6
6
2
7
3
1
2
6
⋯
𝑓
5
(
𝑥
)
=
l
n
(
𝑥
2
+
𝑥
+
2
)
−
𝑥
+
1
,
𝛼
=
4
.
1
5
2
5
9
0
7
4
⋯
𝑓
6
(
𝑥
)
=
e
x
p
(
𝑥
2
+
7
𝑥
−
3
0
)
−
1
,
𝛼
=
1
.
4
0
4
4
9
1
6
5
⋯
𝑓
7
(
𝑥
)
=
c
o
s
(
𝑥
)
2
−
𝑥
5
𝛼
=
1
.
0
8
5
9
8
2
6
8
⋯
𝑓
8
𝑥
(
𝑥
)
=
s
i
n
(
𝑥
)
−
2
,
𝛼
=
0
𝑓
9
(
𝑥
)
=
𝑥
1
0
−
𝑥
3
−
𝑥
+
1
𝛼
=
0
.
5
9
1
4
4
8
0
9
3
⋯
𝑓
1
0
(
𝑥
)
=
s
i
n
(
𝑥
)
−
𝑥
+
1
𝛼
=
2
.
6
3
0
6
6
4
1
5
⋯