Table 2: (a) The errors of the numerical solutions of (2.22 ) by methods {(7.1 ), (3.10 )}, (b) The CPU times (in second) of methods (3.7 )–(3.10 ) for (2.23 ) and (c) The CPU times (in second) of methods {(7.1 ), (3.10 )} for (2.23 ).(a)
(
Δ
𝑣
,
ℎ
)
Gauss Radau IA Radau IIA Lobatto IIIC (
√
𝜋
/
3
0
,
3
/
1
6
)
9
.
0
1
9
3
𝑒
−
0
0
6
3
.
7
2
7
3
𝑒
−
0
0
4
3
.
8
9
6
6
𝑒
−
0
0
4
1
.
4
0
8
3
𝑒
−
0
0
2
(
√
𝜋
/
6
0
,
3
/
3
2
)
5
.
6
7
3
9
𝑒
−
0
0
7
4
.
6
4
9
1
𝑒
−
0
0
5
4
.
9
5
5
8
𝑒
−
0
0
5
3
.
5
4
5
3
𝑒
−
0
0
3
(
√
𝜋
/
1
2
0
,
3
/
6
4
)
3
.
5
5
3
4
𝑒
−
0
0
8
5
.
7
9
3
3
𝑒
−
0
0
6
6
.
2
3
6
0
𝑒
−
0
0
6
8
.
8
9
1
2
𝑒
−
0
0
4
(
√
𝜋
/
2
4
0
,
3
/
1
2
8
)
2
.
2
2
1
7
𝑒
−
0
0
9
7
.
2
2
8
4
𝑒
−
0
0
7
7
.
8
1
8
6
𝑒
−
0
0
7
2
.
2
2
6
1
𝑒
−
0
0
4
(b)
(
Δ
𝑣
,
ℎ
)
Gauss Radau IA Radau IIA Lobatto IIIC (
√
𝜋
/
3
0
,
3
/
1
6
)
7
.
0
7
8
0
𝑒
+
0
0
0
6
.
8
7
5
0
𝑒
+
0
0
0
6
.
9
0
6
0
𝑒
+
0
0
0
6
.
9
3
8
0
𝑒
+
0
0
0
(
√
𝜋
/
6
0
,
3
/
3
2
)
4
.
4
4
6
8
𝑒
+
0
0
1
4
.
4
5
0
0
𝑒
+
0
0
1
4
.
4
7
6
6
𝑒
+
0
0
1
4
.
5
1
7
2
𝑒
+
0
0
1
(
√
𝜋
/
1
2
0
,
3
/
6
4
)
3
.
3
0
3
9
𝑒
+
0
0
2
3
.
3
1
5
6
𝑒
+
0
0
2
3
.
3
2
8
1
𝑒
+
0
0
2
3
.
3
2
6
4
𝑒
+
0
0
2
(
√
𝜋
/
2
4
0
,
3
/
1
2
8
)
2
.
7
1
1
7
𝑒
+
0
0
3
2
.
7
0
4
2
𝑒
+
0
0
3
2
.
7
1
0
9
𝑒
+
0
0
3
2
.
7
2
9
1
𝑒
+
0
0
3
(c)
(
Δ
𝑣
,
ℎ
)
Gauss Radau IA Radau IIA Lobatto IIIC (
√
𝜋
/
3
0
,
3
/
1
6
)
4
.
2
1
8
0
𝑒
+
0
0
0
4
.
2
3
5
0
𝑒
+
0
0
0
4
.
2
6
5
0
𝑒
+
0
0
0
4
.
2
8
2
0
𝑒
+
0
0
0
(
√
𝜋
/
6
0
,
3
/
3
2
)
3
.
0
9
5
3
𝑒
+
0
0
1
3
.
0
2
3
4
𝑒
+
0
0
1
3
.
1
0
3
1
𝑒
+
0
0
1
3
.
1
1
2
5
𝑒
+
0
0
1
(
√
𝜋
/
1
2
0
,
3
/
6
4
)
2
.
7
0
5
5
𝑒
+
0
0
2
2
.
8
4
0
0
𝑒
+
0
0
2
2
.
7
2
1
3
𝑒
+
0
0
2
2
.
7
1
0
5
𝑒
+
0
0
2
(
√
𝜋
/
2
4
0
,
3
/
1
2
8
)
2
.
7
8
2
1
𝑒
+
0
0
3
2
.
8
1
6
4
𝑒
+
0
0
3
2
.
7
9
5
0
𝑒
+
0
0
3
2
.
8
0
0
6
𝑒
+
0
0
3