Theory and Modern Applications
Table 7 Problem 3 : MAEs using ( 2.21a )-( 2.21b ) with \(\pmb{C=\sqrt{\lambda}}\) for \(\pmb{0< x<\frac{1}{2}}\) and \(\pmb{C=\frac {1}{\sqrt{\lambda}}}\) for \(\pmb{\frac{1}{2} \leq x <1}\)
λ | \(\boldsymbol {10^{2}} \) | \(\boldsymbol {10^{4}} \) | \(\boldsymbol {10^{6}} \) | \(\boldsymbol {10^{8}} \) | ||||
|---|---|---|---|---|---|---|---|---|
N | u | \(\boldsymbol {u'}\) | u | \(\boldsymbol {u'}\) | u | \(\boldsymbol {u'}\) | u | \(\boldsymbol {u'}\) |
32 | 3.08e−05 | 1.71e−04 | 1.11e−04 | 2.84e−03 | 5.24e−05 | 1.24e−02 | 1.25e−05 | 3.01e−02 |
64 | 3.96e−06 | 2.10e−05 | 8.40e−06 | 2.29e−04 | 4.06e−06 | 9.84e−04 | 1.22e−06 | 2.89e−03 |
128 | 5.28e−07 | 2.69e−06 | 7.38e−07 | 2.15e−05 | 3.18e−07 | 8.45e−05 | 9.06e−08 | 2.32e−04 |
256 | 6.91e−08 | 3.43e−07 | 7.49e−08 | 2.31e−06 | 2.91e−08 | 8.39e−06 | 7.76e−09 | 2.16e−05 |
Order | 2.93 | 2.97 | 3.30 | 3.22 | 3.45 | 3.33 | 3.55 | 3.43 |