1
1
2
0
2
0
1
1
0
1
2
1
1
()
(
)
()
1,
1,
()
0,
d
K
d
ii
d
−−
−
+
−
=
−
=
(44)
where
()
()
(
)
2
0
0
0
2
1
0
1
1
1
(
)
sin
,
2
2
(
)
2
n
n
i
K
ctg
n
g
+
=
−
−
=
−
−
−
−
−
and
()
()
21
2
2
,0
2
1
()
2
m
i
i
yd
g
−
=
, and for
0
n
()
()
(
)
1
2
2
,
2
1
1
1
()
2
in
mn
n
n
y
e
d
n
−
−
=
−
.
For the solution of SIE (44) we will use the method of discrete singularities
[26,27]. According to this method SIE (44) is equivalent to the following system of
linear equations (SLE)
11
0
1
()
1
(
)
()
,
1,
1;
(45)
()
0,
,
(46)
k
q
q
q
ki
s
oj
q
s
ss
s
j
q
q
qs
s
Vt
Kt
t
Vt
i
j
q
q
tt
Vt
j
q
==
=
+
−
=
=
−
−
==
where:
()
2
2
()
1
V
=
−
;
(47)
21
cos
2
q
s
s
t
q
−
=
are the roots of the Chebyshev polynomial of the first kind, and
cos
q
oj
j
t
q
=
are the roots of the Chebyshev polynomial of the second kind. Taking into
account relation between
2
()
and
()
V
(47) and applying the Gauss quadrature
formula
1
2
1
1
()
()
1
q
q
s
s
G
dG
q
=
−
=
−
, we obtain formulas for coefficients calculation
()
2
,
mn
y
:
()
()
2
2
,0
2
1
11
(
)
,
2
q
ss
m
s
i
i
y
V
t
q
g
=
=
(48)
()
()
(
)
22
,
1
1
1
1
(
)
,
0.
2
q
p
k
in
q
mn
n
p
i
n
y
V
e
n
n
q
−
=
=
−
(49)
From the SLE solution (45), (46), we find
()
q
p
V
, and use it for definition of
()
2
,0
m
y
and
()
2
,
mn
y
(48), (49), that related with required coefficients
()
2
(,,)
n
xd
. In the
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