Theory and Modern Applications
N  + 1 |  | \(\boldsymbol {O(k^{2}+ k^{2}h_{l}+h_{l}^{3})}\) -method ( 16a )-( 16b ) | \(\boldsymbol {O(k^{2}+ h_{l}^{2})}\) -method ( 15a )-( 15b ) | ||||
---|---|---|---|---|---|---|---|
 | α  = 10 | α  = 20 | α  = 40 | α  = 10 | α  = 20 | α  = 40 | |
8 | u | 3.3667 (−05) | 7.7683 (−05) | 1.7212 (−02) | 2.6072 (−04) | 3.0874 (−04) | 2.6133 (−02) |
\(u_{xx}\) | 3.3298 (−04) | 7.6915 (−04) | 1.7290 (−01) | 2.3571 (−04) | 7.0446 (−04) | 2.5645 (−01) | |
16 | u | 2.1139 (−06) | 4.7259 (−06) | 1.0805 (−03) | 8.6976 (−05) | 1.0909 (−04) | 9.5763 (−03) |
\(u_{xx}\) | 2.1334 (−05) | 4.7049 (−05) | 1.0817 (−02) | 1.2171 (−04) | 3.4424 (−04) | 9.4655 (−02) | |
32 | u | 1.3319 (−07) | 2.7901 (−07) | 7.8958 (−05) | 4.1496 (−05) | 5.1293 (−05) | 3.9491 (−03) |
\(u_{xx}\) | 1.5345 (−06) | 2.9686 (−06) | 7.9178 (−04) | 5.4398 (−05) | 1.5469 (−04) | 3.9160 (−02) |