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.
R
EF
ER
EN
C
ES
[
1]
D
a
y
J
T
.
,
“
A
R
ung
e
-
K
ut
t
a
M
e
t
ho
d
f
o
r
t
he
N
um
e
r
i
c
a
l
S
o
l
ut
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o
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o
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he
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ur
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pe
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bo
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c
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f
f
e
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e
n
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i
a
l
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qu
a
t
i
o
n,
”
Co
m
p
ut
e
r
J
o
ur
na
l
,
v
o
l
.
9(
1)
,
pp
.
81
-
83
,
19
9
6
.
[
2]
T
a
g
hv
a
f
a
r
d
H
.
a
nd
E
r
j
a
e
e
H
.
G
.
,
“
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w
o
-
D
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m
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L
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ne
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o
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ne
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r
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r
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t
pr
o
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e
m
,”
I
n
t
e
r
na
t
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o
na
l
J
ou
r
na
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o
f
E
ng
i
ne
e
r
i
ng
and
M
a
t
he
m
at
i
c
a
l
S
c
i
e
nc
e
s
,
v
o
l
.
6
(
2
)
,
pp.
10
3
-
106
,
2
010
.
[
3]
P
a
nde
y
P
.
K.
,
“
A
F
i
ni
t
e
D
i
f
f
e
r
e
nc
e
M
e
t
ho
d
f
o
r
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um
e
r
i
c
a
l
S
o
l
u
t
i
o
n
o
f
G
o
ur
s
a
t
P
r
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bl
e
m
o
f
P
a
r
t
i
a
l
D
i
f
f
e
r
e
n
t
i
a
l
E
qua
t
i
o
n
,
”
O
pe
n
A
c
c
e
s
s
L
i
b
r
ar
y
J
ou
r
na
l
,
v
o
l
.
1
(
0
6)
,
p.
1
,
2014
.
[
4]
W
a
z
w
a
z
A
.
M
.
,
“
O
n
t
h
e
N
um
e
r
i
c
a
l
S
o
l
u
t
i
o
n
f
o
r
t
he
G
o
ur
s
a
t
P
r
o
bl
e
m
,”
A
p
pl
i
e
d
M
a
t
he
m
at
i
c
s
and
C
om
p
ut
at
i
on
,
v
o
l
.
59(
1)
,
pp
.
89
-
95
,
19
93
.
[
5]
W
a
z
w
a
z
A
.
M.
,
“
T
he
V
a
r
i
a
t
i
o
na
l
I
t
e
r
a
t
i
o
n
M
e
t
ho
d
f
o
r
a
R
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l
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a
b
l
e
T
r
e
a
t
m
e
n
t
o
f
L
i
ne
a
r
a
n
d
N
o
nl
i
ne
a
r
G
o
ur
s
a
t
P
r
o
bl
e
m
,”
A
pp
l
i
e
d
M
at
he
m
a
t
i
c
s
and
C
om
p
ut
a
t
i
on
,
v
o
l
.
193
(
2
)
pp.
4
55
-
462
,
2
007
.
[
6]
A
hm
a
d
J
.
a
nd
M
u
s
h
t
a
q
M
.
,
“
E
x
a
c
t
S
o
l
u
t
i
o
n
o
f
L
i
ne
a
r
a
n
d
N
o
n
-
l
i
ne
a
r
G
o
ur
s
a
t
P
r
o
bl
e
m
s
,”
U
ni
v
e
r
s
a
l
J
ou
r
na
l
of
C
om
put
at
i
ona
l
M
at
he
m
a
t
i
c
,
v
o
l
.
3
(
1
)
,
pp
.
14
-
17
,
2015
.
[
7]
T
uc
kw
e
l
l
H
.
C.
,
“
N
um
e
r
i
c
a
l
s
o
l
ut
i
o
ns
o
f
s
o
m
e
hy
pe
r
bo
l
i
c
s
t
o
c
ha
s
t
i
c
p
a
r
t
i
a
l
d
i
f
f
e
r
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n
t
i
a
l
e
qua
t
i
o
ns
w
i
t
h
m
i
xe
d
de
r
i
v
a
t
i
v
e
s
i
nc
l
ud
i
ng
s
i
n
e
-
G
o
r
do
n
e
qu
a
t
i
o
n,
”
C
or
ne
l
l
U
n
i
v
e
r
s
i
t
y
L
i
br
ar
y
.
20
15
.
[
8]
P
e
r
f
i
l
i
e
v
a
I
.
,
F
uz
z
y
ap
pr
o
ac
h
t
o
s
ol
u
t
i
on
of
d
i
f
f
e
r
e
nt
i
al
e
quat
i
o
ns
w
i
t
h
i
m
pr
e
c
i
s
e
da
t
a:
ap
pl
i
c
a
t
i
on
t
o
r
e
e
f
g
r
ow
t
h
pr
ob
l
e
m
.
A
c
a
de
m
i
c
P
r
e
s
s
,
A
m
s
t
e
r
da
m
,
pp.
2
75
-
300
,
2003
.
[
9]
P
e
r
f
i
l
i
e
v
a
I
.
,
F
uz
z
y
T
r
an
s
f
or
m
s
.
R
ou
gh
and
F
uz
z
y
R
e
as
o
ni
n
g:
R
ou
g
h
v
e
r
s
us
F
uz
z
y
.
S
pr
i
ng
e
r
-
V
e
r
l
a
g
,
2
004
.
[
10]
P
e
r
f
i
l
i
e
v
a
I
.
a
nd
V
a
l
a
´
s
e
k
R
.
,
“
F
uz
z
y
T
r
a
ns
f
o
r
m
s
i
n
R
e
m
o
v
i
ng
N
o
i
s
e
,
”
C
om
p
ut
at
i
ona
l
I
n
t
e
l
l
i
ge
nc
e
,
T
he
or
y
an
d
A
ppl
i
c
a
t
i
o
ns
(
A
dv
anc
e
s
i
n
S
of
t
C
om
pu
t
i
n
g)
,
S
pr
i
ng
e
r
-
V
e
r
l
a
g
,
2
004
.
[
11]
P
e
r
f
i
l
i
e
v
a
I
.
a
nd
K
r
e
i
no
v
i
c
h
V
.
,
“
F
uz
z
y
t
r
a
n
s
f
o
r
m
s
o
f
hi
g
he
r
o
r
d
e
r
a
pp
r
o
xi
m
a
t
e
d
e
r
i
v
a
t
i
v
e
s
:
A
t
he
o
r
e
m
,
”
F
uz
z
y
Se
t
s
and
Sy
s
t
e
m
s
,
v
o
l
.
180
(
1)
,
pp
.
55
-
68
,
2
011
.
[
12]
P
e
r
f
i
l
i
e
v
a
I.
,
“
F
uz
z
y
t
r
a
n
s
f
o
r
m
s
:
T
he
o
r
y
a
nd
a
pp
l
i
c
a
t
i
o
ns
,
”
F
uz
z
y
Se
t
s
a
nd
S
y
s
t
e
m
s
,
v
o
l
.
15
7
(
8
)
,
pp
.
99
3
-
1023
,
2
006
.
[
13]
P
a
t
a
nè
G
.
,
“
F
uz
z
y
t
r
a
n
s
f
o
r
m
a
n
d
l
e
a
s
t
-
s
qu
a
r
e
s
a
p
pr
o
xi
m
a
t
i
o
n:
A
na
l
o
g
i
e
s
,
d
i
f
f
e
r
e
nc
e
s
,
a
nd
g
e
ne
r
a
l
i
z
a
t
i
o
ns
,
”
F
uz
z
y
Se
t
s
a
nd
Sy
s
t
e
m
s
,
v
o
l
.
180
(
1
)
,
pp
.
41
-
54
,
2011
.
[
14]
K
ha
s
t
a
n
A
.
,
P
e
r
f
i
l
i
e
v
a
I
.
,
a
nd
A
l
i
j
a
ni
Z
.
,
“
A
ne
w
f
uz
z
y
a
pp
r
o
xi
m
a
t
i
o
n
m
e
t
ho
d
t
o
C
a
u
c
hy
pr
o
bl
e
m
s
by
f
uz
z
y
t
r
a
ns
f
o
r
m
,
”
F
uz
z
y
Se
t
s
a
nd
Sy
s
t
e
m
s
,
v
o
l
.
288
,
pp
.
75
-
95
,
2
016
.
[
15]
C
o
r
o
i
a
nu
L
.
a
nd
S
t
e
f
a
n
i
ni
L
.
,
“
G
e
n
e
r
a
l
a
pp
r
o
xi
m
a
t
i
o
n
o
f
f
uz
z
y
num
be
r
s
by
F
-
t
r
a
ns
f
o
r
m
,
”
F
uz
z
y
Se
t
s
and
S
y
s
t
e
m
s
,
v
o
l
.
288
,
pp.
4
6
-
74
,
2
0
16
.
[
16]
P
e
r
f
i
l
i
e
v
a
I
.
,
F
uz
z
y
t
r
ans
f
o
r
m
s
and
un
i
v
e
r
s
al
a
ppr
o
x
i
m
at
i
on
.
E
U
S
F
L
A
T
c
o
nf
e
r
e
nc
e
,
pp
.
529
-
533
,
200
3
.
[
17]
Z
a
de
h
L
.
,
F
uz
z
y
s
e
t
t
he
o
r
y
.
I
n
f
or
m
at
i
on
an
d
C
o
nt
r
o
l
,
pp
.
338
–
353
,
1965
.
[
18]
W
a
z
w
a
z
A
.
M.
,
P
ar
t
i
a
l
D
i
f
f
e
r
e
nt
i
al
E
qua
t
i
ons
and
So
l
i
t
a
r
y
W
av
e
s
T
he
or
y
.
B
e
i
j
i
ng
:
H
i
g
he
r
o
f
E
duc
a
t
i
o
n
P
r
e
s
s
a
nd
S
pr
i
ng
e
r
-
V
e
r
l
a
g
B
e
r
l
i
n
H
e
i
de
l
b
e
r
g
.
200
9.
[
19]
W
a
z
w
a
z
A
.
M.
,
“
T
h
e
v
a
r
i
a
t
i
o
na
l
i
t
e
r
a
t
i
o
n
m
e
t
ho
d
f
o
r
a
r
e
l
i
a
b
l
e
t
r
e
a
t
m
e
nt
o
f
t
he
l
i
ne
a
r
a
n
d
t
he
no
nl
i
n
e
a
r
G
o
ur
s
a
t
pr
o
bl
e
m
,
”
A
pp
l
i
e
d
M
at
he
m
at
i
c
s
and
C
om
p
ut
at
i
on
,
v
o
l
.
19
3(
2
)
,
p
p
.
455
-
462
,
2007
.
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