Theory and Modern Applications
Table 5 Problem 3 : MAEs using ( 2.7a )-( 2.7b ) 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 | 2.50e−04 | 2.15e−03 | 9.24e−04 | 2.71e−02 | 1.74e−02 | 1.36e−01 | 1.97e−01 | 1.48e+00 |
64 | 6.12e−05 | 5.72e−04 | 2.84e−04 | 7.84e−03 | 2.43e−04 | 1.74e−02 | 7.29e−02 | 7.06e−01 |
128 | 1.50e−05 | 1.45e−04 | 7.31e−05 | 1.96e−03 | 1.85e−05 | 4.65e−03 | 3.26e−06 | 8.23e−03 |
256 | 3.74e−06 | 3.64e−05 | 1.84e−05 | 4.91e−04 | 4.72e−06 | 1.16e−03 | 8.49e−07 | 2.07e−03 |
Order | 2.01 | 1.99 | 1.99 | 2.00 | 1.97 | 2.00 | 1.94 | 1.99 |