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.
If
c
o
m
pa
r
e
d
t
o
ge
n
e
t
i
c
a
l
go
ri
t
hm
s
,
i
t
i
s
i
de
a
l
e
ff
i
c
i
e
n
c
y
i
n
a
c
c
ur
a
t
e
c
a
l
c
ul
a
t
i
o
n
s
a
nd
i
s
e
a
s
y
t
o
i
m
pl
e
m
e
n
t
.
T
h
e
P
a
rt
i
c
l
e
s
w
a
r
m
o
pt
i
m
i
z
a
t
i
o
n
(P
S
O
)
a
l
go
r
i
t
hm
i
s
de
ve
l
o
pm
e
n
t
f
o
r
ge
n
e
t
i
c
a
l
go
r
i
t
hm
s
,
w
h
e
r
e
c
r
o
s
s
o
ve
r
,
m
ut
a
t
i
o
n
w
a
s
c
a
n
c
e
l
e
d
a
n
d
i
s
t
h
e
r
e
f
o
r
e
w
i
de
l
y
us
e
d
t
o
s
o
l
ve
s
c
i
e
n
t
i
f
i
c
p
r
o
b
l
e
m
s
a
nd
i
s
us
e
d
t
o
s
t
udy
a
n
d
a
pp
l
y
pa
r
t
i
a
l
di
f
f
e
r
e
n
t
i
a
l
e
qua
t
i
o
n
s
[
14].
T
h
e
F
i
g
u
r
e
1
i
l
l
us
t
r
a
t
e
s
t
h
e
b
a
s
i
c
i
de
a
t
ha
t
s
t
a
r
t
s
f
r
o
m
r
a
ndo
m
s
o
l
ut
i
o
n
t
o
o
pt
i
m
a
l
s
o
l
ut
i
o
n
a
f
t
e
r
c
o
n
t
i
nuo
us
r
e
pe
t
i
t
i
o
n
a
nd
e
v
a
l
ua
t
i
o
n
f
i
t
n
e
s
s
[14]
:
F
i
gu
r
e
1
.
P
S
O
a
l
go
r
i
t
h
m
f
o
r
s
o
l
ut
i
o
n
t
h
e
o
pt
i
m
a
l
2.
M
A
TH
EM
A
TI
C
A
L
M
O
D
EL
:
T
h
i
s
e
qua
t
i
o
n
(K
S
)
w
a
s
de
r
i
v
e
d
t
hr
o
ugh
S
i
v
a
s
h
i
n
s
ky
a
s
a
pa
ra
di
g
m
f
o
r
pl
a
n
e
f
l
a
m
e
s
pr
e
a
d
[15]
,
a
n
d
by
K
ur
a
m
o
t
o
a
s
a
pa
t
t
e
rn
f
o
r
p
ha
s
e
di
s
o
r
de
r
i
n
r
e
a
c
t
i
o
n
pr
o
pa
g
a
t
i
o
n
s
y
s
t
e
m
s
[16
,
17].
T
h
e
K
u
r
a
m
o
t
o
-
S
i
v
a
s
h
i
n
s
ky
e
qua
t
i
o
n
ha
s
m
a
n
y
a
ppl
i
c
a
t
i
o
n
s
i
n
v
a
ri
o
u
s
ph
y
s
i
c
a
l
,
s
c
i
e
nt
i
f
i
c
a
n
d
e
n
g
i
n
e
e
r
i
ng
p
h
e
n
o
m
e
na
,
s
uc
h
a
s
r
e
a
c
t
i
o
n
d
i
f
f
us
i
o
n
s
y
s
t
e
m
s
,
f
l
ow
of
t
h
i
n
l
i
qu
i
d
m
e
m
b
ra
ne
s
[18]
a
nd
i
n
t
h
e
m
o
de
l
o
f
di
f
f
us
i
o
n
a
n
d
c
ha
o
s
[19
-
22]
.
M
a
n
y
a
ut
h
o
r
s
h
a
v
e
s
t
udi
e
d
K
ur
a
m
o
t
o
-
S
i
v
a
s
h
i
n
s
ky
e
qua
t
i
o
n
n
u
m
e
ri
c
a
l
l
y
i
n
s
e
ve
r
a
l
d
i
f
fe
r
e
nt
m
e
t
h
o
ds
H
o
m
o
t
o
p
y
P
e
r
t
u
r
b
a
t
i
o
n
M
e
t
h
o
d
,
A
do
m
i
a
n
D
e
c
o
m
po
s
i
t
i
o
n
M
e
t
h
o
d
,
D
i
f
f
e
r
e
n
t
i
a
l
T
ra
n
s
f
o
r
m
M
e
t
h
o
d
[
23
,
2
4].
Co
n
s
i
de
r
t
h
e
K
u
ra
m
o
t
o
-
S
i
v
a
s
h
i
n
s
ky
e
qua
t
i
o
n
w
i
t
h
[25
]:
Co
n
s
i
de
r
t
h
e
K
u
ra
m
o
t
o
-
S
i
v
a
s
h
i
n
s
ky
e
qua
t
i
o
n
w
i
t
h
[27
]:
(1)
T
h
e
i
ni
t
i
a
l
c
o
n
d
i
t
i
o
n
a
n
d
b
o
un
da
r
y
c
o
n
di
t
i
o
n
a
r
e
t
a
ke
n
a
w
a
y
f
r
o
m
t
h
e
e
xa
c
t
s
o
l
ut
i
o
n
[
26
-
28]
:
(
)
√
(
(
(
)
)
(
(
)
)
)
(2)
T
o
i
l
l
us
t
ra
t
e
t
h
e
m
a
i
n
i
de
a
o
f
t
h
e
(N
E
M
)
m
e
t
h
o
d
by
t
a
ki
ng
t
he
n
e
xt
d
i
f
fe
r
e
nt
i
a
l
e
qu
a
t
i
o
n
:
(
)
(3)
W
h
e
r
e
M
i
s
a
n
o
n
l
i
n
e
a
r
t
e
rm
,
w
e
a
r
e
a
s
s
u
m
i
n
g
t
ha
t
M
i
n
(1)
r
e
p
r
e
s
e
n
t
t
h
e
s
e
r
i
e
s
f
o
r
m
:
(
∑
)
(
)
∑
[
(
∑
)
(
∑
)
]
(4)
C
a
n
b
e
de
c
a
y
e
d
de
c
o
m
po
s
e
d
t
h
e
n
o
nl
i
n
e
a
r
o
pe
ra
t
o
r
M
a
s
:
∑
(
)
∑
[
(
∑
)
(
∑
)
]
(5)
By
c
o
m
pe
n
s
a
t
i
o
n
(4
)
a
n
d
(5)
i
n
(3)
,
ge
t
o
n:
Evaluation Warning : The document was created with Spire.PDF for Python.
In
do
n
e
s
i
a
n
J
E
l
e
c
E
ng
&
Co
m
p
S
c
i
IS
S
N
:
2502
-
4752
Sol
v
i
ng
Kur
am
ot
o
–
Si
v
as
hi
ns
k
y
e
quat
i
on
b
y
t
he
ne
w
i
t
e
r
at
i
v
e
m
e
t
hod
and…
(
Kar
am
A
d
e
l
A
be
d
)
711
{
(
)
(
(
)
)
(
)
(
(
)
(
)
)
(
(
)
)
(
)
(
(
)
(
)
(
)
)
(
(
)
(
)
}
(6)
(
(
(
)
(
)
(
)
)
(
(
(
)
(
)
(
)
)
}
(7)
T
o
u
n
de
r
s
t
a
nd
t
h
e
dup
l
i
c
a
t
e
r
e
l
a
t
i
o
n
i
n
t
h
e
f
o
l
l
ow
i
n
g
m
a
nn
e
r:
W
h
e
r
e
:
∑
(
∑
)
(8)
T
h
e
n
-
b
o
r
de
r
s
s
o
l
ut
i
o
n
s
o
f
(4)
i
s
gi
v
e
n
by
,
t
h
e
c
o
n
v
e
r
ge
n
c
e
o
f
t
hi
s
t
e
c
hn
i
q
ue
i
n
[
29
-
31].
3.
A
P
P
LI
C
A
TI
O
N
In
t
hi
s
p
a
rt
,
w
e
e
n
f
o
r
c
e
m
e
n
t
t
o
s
o
l
ve
(x,
t
)
t
h
e
i
ni
t
i
a
l
c
o
n
d
i
t
i
o
n
s
w
h
i
c
h
s
a
t
i
s
fy
i
n
g
(1)
:
(
)
√
[
(
(
)
)
(
(
)
)
]
(9)
N
ow
,
by
t
h
e
i
nt
e
g
r
a
l
f
o
r
t
h
e
(1)
,
w
e
ge
t
:
(
)
∫
(
(
)
)
∫
(
)
W
i
t
h
t
h
e
i
ni
t
i
a
l
c
o
n
d
i
t
i
o
n
s
i
n
(10)
w
e
ge
t
:
(
)
∫
(
)
∫
(
)
(10)
A
f
t
e
r
s
o
l
v
i
n
g
(11)
w
e
ge
t
:
{
(
)
(
)
(
√
(
√
(
)
(
)
(
)
√
(
)
(
)
√
(
)
(
)
)
)
}
(11)
N
ow
,
w
e
w
o
r
k
t
o
f
i
n
d
t
h
e
b
o
r
de
r
s
e
c
o
n
d:
(
)
∫
(
(
)
(
)
)
(
(
)
)
(
12
)
T
h
e
n
{
(
)
(
)
(
(
(
)
(
)
(
)
√
(
)
)
)
}
(13)
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2502
-
4752
In
do
n
e
s
i
a
n
J
E
l
e
c
E
ng
&
Co
m
p
S
c
i
,
V
o
l
.
19
,
N
o
.
2
,
A
ugus
t
20
20
:
709
-
714
712
A
n
d
t
h
e
f
i
na
l
l
y
w
e
f
i
n
d
Y
3
:
{
(
)
(
)
(
(
(
)
(
)
(
)
√
(
)
(
)
}
(14)
It
w
a
s
fo
un
d
t
h
a
t
t
h
e
e
rr
o
r
i
n
t
h
e
n
um
e
r
i
c
a
l
m
e
t
h
o
d
r
e
a
c
h
e
d
10
-
5
a
t
i
t
s
l
o
w
e
s
t
l
e
v
e
l
a
n
d
10
-
9
a
t
i
t
s
b
e
s
t
,
a
s
s
h
o
w
n
i
n
T
a
b
l
e
1
a
n
d
F
i
gu
r
e
s
2
a
n
d
3.
T
a
b
l
e
1
.
A
b
s
o
l
ut
e
e
rr
o
r
o
f
t
h
e
|
|
by
us
i
n
g
pa
ra
m
e
t
e
r
s
√
,
w
i
t
h
3
nd
o
rde
r
a
t
t
=
0.
1
T
H
0
.
1
0
.
2
0
.
3
0
.
4
0
.
5
8
4
.
5
6
4
0
0
0
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1
0
-
6
1
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4
0
9
9
0
0
*
1
0
-
5
3
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0
5
9
8
0
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1
0
-
5
5
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5
6
4
7
0
0
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1
0
-
5
9
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0
2
8
5
0
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1
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-
5
15
2
.
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1
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-
8
6
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7
0
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1
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1
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4
7
0
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1
0
-
7
2
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7
4
0
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1
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-
7
4
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4
2
0
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1
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-
7
17
3
.
0
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1
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-
9
1
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4
0
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8
3
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7
0
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8
5
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9
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6
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20
1
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9
2
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0
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-
9
0
2
.
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1
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0
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1
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1
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1
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1
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1
0
-
9
1
.
0
0
0
0
0
0
*
1
0
-
9
F
i
gu
r
e
2
.
T
h
e
f
un
c
t
i
o
n
(
)
f
o
r
t
h
e
t
w
o
bo
r
de
r
s
a
pp
r
o
xi
m
a
t
i
o
n
(
-
2)
b
y
us
i
n
g
N
IM
,
w
h
e
n
t
=
0
.
1
F
i
gu
r
e
3
.
T
h
e
a
b
s
o
l
ut
e
e
rr
o
r
f
o
r
t
h
e
t
w
o
b
o
r
de
r
s
a
pp
r
o
xi
m
a
t
i
o
n
(Y
-
2)
b
e
t
w
e
e
n
N
IM
a
n
d
t
h
e
e
xa
c
t
s
o
l
ut
i
o
n
w
h
e
n
t
=
0.
1
4.
S
U
G
G
ES
TED
M
ET
H
O
D
:
T
h
e
b
a
s
i
c
i
de
a
of
t
h
e
pr
o
po
s
a
l
t
e
c
h
ni
que
i
s
t
o
f
i
n
d
t
h
e
o
pt
i
m
a
l
pa
r
a
m
e
t
e
r
s
of
n
o
n
l
i
n
e
a
r
K
u
ra
m
o
t
o
–
S
i
v
a
s
h
i
n
s
ky
e
qua
t
i
o
n
(ks
e
)
us
i
n
g
t
h
e
(P
S
O
)
a
l
go
r
i
t
hm
w
i
t
h
t
h
e
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3
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13
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83
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005
.
[
8]
A
.
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n
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l
.
458
,
no
.
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,
pp
.
933
–
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.
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9]
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I
C
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,
15
M
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2016
,
I
s
bn;
978
-
81
-
932074
-
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-
2.
[
13]
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hu
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19]
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l
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4,
p
p.
34
9
3
-
3500,
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e
c
2018
.
[
20]
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l
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o
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ug
2019.
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21]
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2
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-
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13.
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no
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,
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,
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24]
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[
25]
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o
ur
na
l
,
p
p.
15
81
–
1
589
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.
[
26]
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.
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.
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.
M
at
h.
C
om
p
ut
.
212
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,
458
–
469
.
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27]
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