Theory and Modern Applications
Table 5 The MAEs for Example 5 at \(\pmb{t=1.0, \eta=0.94}\) (quasi-variable mesh)
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  = 1 | α  = 2 | α  = 1 | α  = 2 | |
8 | u | 1.8743 (−04) | 5.4079 (−04) | 3.6061 (−03) | 8.7376 (−03) |
\(u_{rr}\) | 1.4353 (−03) | 8.2498 (−03) | 8.6067 (−02) | 7.9741 (−02) | |
16 | u | 1.7017 (−05) | 4.5019 (−05) | 6.8621 (−04) | 1.6912 (−03) |
\(u_{rr}\) | 1.5498 (−04) | 1.3071 (−03) | 2.6282 (−02) | 4.7895 (−02) | |
32 | u | 3.1833 (−06) | 7.4946 (−06) | 1.2889 (−04) | 3.5410 (−04) |
\(u_{rr}\) | 5.1980 (−05) | 4.3430 (−04) | 1.1033 (−02) | 3.0090 (−02) | |