Theory and Modern Applications
Table 2 The approximate and exact solutions of \(\pmb{h(x,t)}\) for Example 5.2 for different values of α and \(\pmb{y=0.4}\)
x | t | α  = 0.75 | α  = 0.9 | α  = 1 | |
|---|---|---|---|---|---|
Numerical | Exact | ||||
0.5 | 0.3 | 1.6256 | 1.74178 | 1.82217 | 1.82212 |
0.6 | 1.27791 | 1.31047 | 1.35131 | 1.34986 | |
0.9 | 1.10414 | 1.02931 | 1.0105 | 1 | |
1 | 0.3 | 2.68017 | 2.8717 | 3.00424 | 3.00417 |
0.6 | 2.10692 | 2.1606 | 2.22793 | 2.22554 | |
0.9 | 1.82042 | 1.69705 | 1.66603 | 1.64872 | |
1.5 | 0.3 | 4.41885 | 4.73464 | 4.95316 | 4.95303 |
0.6 | 3.47372 | 3.56223 | 3.67323 | 3.6693 | |
0.9 | 3.00136 | 2.79796 | 2.74682 | 2.71828 | |