Research Article
Approximate Analytic Solution for the KdV and Burger Equations with the Homotopy Analysis Method
Table 2
Comparison of the HAM solution with exact solution when
and
, respectively.
| | | Exact solution | HAM solution | Absolute error |
| | 0 | −∞
−100
−50
−20
0
20
50
100
200
∞ | 1.
1.
0.99999999998611
0.99995460229829
0.5
0.00004539770170
.
.
0. | 1.
1.
0.9999999999
0.9999546021
0.5
0.0000453978
0.
0.
0. | 0.
0.
0
0.
0.
0. |
| | 0.25 | −∞
−100
−50
−20
0
20
50
100
200
300 | 1.
1.
0.9999999999999
0.9999559989777
0.5078118671525
0.0000468387124
0.
0.
0 | 1.
1.
0.99999999998
0.99995735253
0.51561991572
0.00004832563
0 | 0.
0.
0 |
| | 0.5 | −∞
−100
−50
−20
0
20
50
100
200
300 | 1.
1.
0.999999999986
0.999957352689
0.515619921465
0.000048325461
0.
0.
0. | 1.
1.
0.99999999998
0.99995993630
0.53120937337
0.00005144221
| 0.
0.
|
| | 0.75 | −∞
−100
−50
−20
0
20
50
100
200
300 | 1.
1.
0.999999999987
0.99995866475
0.523420357539
0.000049859400
0.
0. | 1.
1.
0.99999999998
0.99996236355
0.54673815197
0.00005475976
| 0.
0.
|
| | 1 | −∞
−100
−50
−20
0
20
50
100
200
300 | 1.
1.
0.999999999987744
0.9999599364569929
0.5312093848251956
0.000051442026872461355
0.
0.
0. | 1.
1.
0.9999999999
0.9999646437
0.5621765008
0.0000582912
| 0.
0.
|
|
|
