Theory and Modern Applications
Table 9 The MAEs for Example 9 at \(\pmb{t=4.0, \eta=0.92}\) (quasi-variable mesh)
N  + 1 |  | \(\boldsymbol {O(k^{2}+ k h_{l}+h_{l}^{3})}\) -method ( 37a )-( 37b ) | \(\boldsymbol {O(k^{2}+ h_{l}^{2})}\) -method ( 36a )-( 36b ) | ||||
|---|---|---|---|---|---|---|---|
|  | α  = 1 | α  = 5 | α  = 10 | α  = 1 | α  = 5 | α  = 10 | |
8 | u | 2.5627 (−05) | 3.5373 (−05) | 7.1052 (−05) | 1.1611 (−04) | 1.1059 (−04) | 8.9291 (−05) |
\(u_{xx}-u_{t}\) | 2.8854 (−05) | 8.8904 (−05) | 4.3557 (−04) | 1.6636 (−05) | 4.6297 (−05) | 2.4532 (−04) | |
16 | u | 1.6009 (−06) | 2.2252 (−06) | 4.5252 (−06) | 4.3184 (−05) | 4.3903 (−05) | 4.6318 (−05) |
\(u_{xx}-u_{t}\) | 1.8900 (−06) | 5.7189 (−06) | 2.8222 (−05) | 2.0745 (−06) | 8.1349 (−06) | 3.5144 (−05) | |
32 | u | 9.1931 (−08) | 1.3617 (−07) | 2.9842 (−07) | 2.1699 (−05) | 2.2259 (−05) | 2.4254 (−05) |
\(u_{xx}-u_{t}\) | 1.4804 (−07) | 4.2072 (−07) | 2.0094 (−06) | 1.7714 (−06) | 6.1484 (−06) | 2.7953 (−05) | |