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Advances in Numerical Analysis
Table of Contents
Advances in Numerical Analysis
/
2012
/
Article
/
Tab 1
/
Research Article
Further Development of Jarratt Method for Solving Nonlinear Equations
Table 1
Test functions and their roots.
Functions
Roots
𝑓
1
(
𝑥
)
=
e
x
p
(
𝑥
)
s
i
n
(
𝑥
)
+
l
n
(
1
+
𝑥
2
)
𝛼
=
0
𝑓
2
(
𝑥
)
=
(
𝑥
2
−
1
)
−
1
−
1
√
𝛼
=
2
𝑓
3
(
𝑥
)
=
(
𝑥
−
2
)
(
𝑥
1
0
+
𝑥
+
1
)
e
x
p
(
−
𝑥
−
1
)
𝛼
=
2
𝑓
4
(
𝑥
)
=
(
𝑥
+
1
)
e
x
p
(
s
i
n
(
𝑥
)
)
−
𝑥
2
e
x
p
(
c
o
s
(
𝑥
)
)
−
1
𝛼
=
0
𝑓
5
(
𝑥
)
=
s
i
n
(
𝑥
)
2
−
𝑥
2
+
1
𝛼
=
1
.
4
0
4
4
9
1
6
5
…
𝑓
6
(
𝑥
)
=
e
x
p
(
−
𝑥
)
−
c
o
s
(
𝑥
)
,
𝛼
=
−
0
.
6
6
6
2
7
3
1
2
6
…
𝑓
7
(
𝑥
)
=
l
n
(
𝑥
2
+
𝑥
+
2
)
−
𝑥
+
1
𝛼
=
4
.
1
5
2
5
9
0
7
4
…
𝑓
8
(
𝑥
)
=
𝑥
1
0
−
2
𝑥
3
−
𝑥
+
1
𝛼
=
0
.
5
9
1
4
4
8
0
9
3
…
𝑓
9
(
𝑥
)
=
c
o
s
(
𝑥
)
2
−
5
−
1
𝑥
𝛼
=
1
.
0
8
5
9
8
2
6
8
…
𝑓
1
0
(
𝑥
)
=
s
i
n
(
𝑥
)
−
2
−
1
𝑥
𝛼
=
0