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International Scholarly Research Notices
/
2012
/
Article
/
Tab 4
/
Research Article
A New Efficient Method for Solving Two-Dimensional Burgers' Equation
Table 4
The LTNHPM results for
𝑣
(
𝑥
,
𝑦
,
𝑡
)
for the first five approximations with
𝑅
=
1
.
(
𝑥
,
𝑦
)
𝑡
=
0
.
0
1
𝑡
=
0
.
5
𝑡
=
2
𝑣
∗
(
𝑥
,
𝑦
,
𝑡
)
|
𝑣
∗
−
𝑣
|
𝑣
∗
(
𝑥
,
𝑦
,
𝑡
)
|
𝑣
∗
−
𝑣
|
𝑣
∗
(
𝑥
,
𝑦
,
𝑡
)
|
𝑣
∗
−
𝑣
|
(
0
.
1
,
0
.
1
)
0
.
8
7
5
0
1
9
5
3
1
2
1
𝐸
−
1
0
0
.
8
7
5
9
7
6
5
4
2
4
2
𝐸
−
1
0
0
.
8
7
8
9
0
0
6
2
5
1
4
𝐸
−
6
(
0
.
5
,
0
.
1
)
0
.
8
7
8
1
4
3
8
7
1
3
3
𝐸
−
9
0
.
8
7
9
1
0
0
0
9
4
1
3
𝐸
−
9
0
.
8
8
2
0
1
9
4
7
3
0
4
𝐸
−
6
(
0
.
9
,
0
.
1
)
0
.
8
8
1
2
6
4
2
7
9
3
1
𝐸
−
1
0
0
.
8
8
2
2
1
8
5
2
2
0
2
𝐸
−
1
0
0
.
8
8
5
1
2
9
6
1
7
0
4
𝐸
−
6
(
0
.
3
,
0
.
3
)
0
.
8
7
5
0
1
9
5
3
1
2
1
𝐸
−
1
0
0
.
8
7
5
9
7
6
5
4
2
4
2
𝐸
−
1
0
0
.
8
7
8
9
0
0
6
2
5
1
4
𝐸
−
6
(
0
.
7
,
0
.
3
)
0
.
8
7
8
1
4
3
8
7
1
3
3
𝐸
−
9
0
.
8
7
9
1
0
0
0
9
4
1
3
𝐸
−
9
0
.
8
8
2
0
1
9
4
7
3
0
4
𝐸
−
6
(
0
.
1
,
0
.
5
)
0
.
8
7
1
8
9
5
1
7
2
2
2
𝐸
−
9
0
.
8
7
2
8
5
1
7
7
6
0
2
𝐸
−
9
0
.
8
7
5
7
7
6
9
5
4
8
4
𝐸
−
6
(
0
.
5
,
0
.
5
)
0
.
8
7
5
0
1
9
5
3
1
2
1
𝐸
−
1
0
0
.
8
7
5
9
7
6
5
4
2
4
2
𝐸
−
1
0
0
.
8
7
8
9
0
0
6
2
5
1
4
𝐸
−
6
(
0
.
9
,
0
.
5
)
0
.
8
7
8
1
4
3
8
7
1
3
3
𝐸
−
9
0
.
8
7
9
1
0
0
0
9
4
1
3
𝐸
−
9
0
.
8
8
2
0
1
9
4
7
3
0
4
𝐸
−
6
(
0
.
3
,
0
.
7
)
0
.
8
7
1
8
9
5
1
7
2
2
2
𝐸
−
1
0
0
.
8
7
2
8
5
1
7
7
6
0
2
𝐸
−
9
0
.
8
7
5
7
7
6
9
5
4
8
4
𝐸
−
6
(
0
.
7
,
0
.
7
)
0
.
8
7
5
0
1
9
5
3
1
2
1
𝐸
−
1
0
0
.
8
7
5
9
7
6
5
4
2
4
2
𝐸
−
1
0
0
.
8
7
8
9
0
0
6
2
5
1
4
𝐸
−
6
(
0
.
1
,
0
.
9
)
0
.
8
6
8
7
7
4
6
8
6
4
6
𝐸
−
1
0
0
.
8
6
9
7
2
9
6
8
9
2
4
𝐸
−
1
0
0
.
8
7
2
6
5
2
3
4
6
4
4
𝐸
−
6
(
0
.
5
,
0
.
9
)
0
.
8
7
1
8
9
5
1
7
2
2
1
𝐸
−
9
0
.
8
7
2
8
5
1
7
7
6
0
2
𝐸
−
9
0
.
8
7
5
7
7
6
9
5
4
8
4
𝐸
−
6
(
0
.
9
,
0
.
9
)
0
.
8
7
5
0
1
9
5
3
1
2
1
𝐸
−
1
0
0
.
8
7
5
9
7
6
5
4
2
4
2
𝐸
−
1
0
0
.
8
7
8
9
0
0
6
2
5
1
4
𝐸
−
6