Theory and Modern Applications
λ | N |  | Uniform mesh ( C  = 1) | Quasi-variable mesh ( C  = 0.7) | ||
---|---|---|---|---|---|---|
MAE | RMSE | MAE | RMSE | |||
1 | 16 | u | 1.59e−07 | 1.20e−08 | 1.01e−06 | 4.22e−08 |
\(u' \) | 5.68e−07 | 3.72e−07 | 3.29e−06 | 1.59e−06 | ||
32 | u | 1.00e−08 | 2.13e−10 | 1.11e−07 | 1.20e−09 | |
\(u' \) | 3.55e−08 | 1.34e−08 | 3.52e−07 | 9.15e−08 | ||
64 | u | 6.29e−10 | 3.54e−12 | 1.29e−08 | 3.57e−11 | |
order | 4.00 | 5.91 | 3.10 | 5.07 | ||
\(u' \) | 2.23e−09 | 4.49e−10 | 4.10e−08 | 5.47e−09 | ||
order | 4.00 | 4.90 | 3.10 | 4.06 | ||
10 | 16 | u | 9.90e−07 | 1.24e−07 | 2.08e−06 | 1.58e−07 |
\(u' \) | 4.63e−06 | 3.69e−06 | 8.43e−06 | 5.61e−06 | ||
32 | u | 6.20e−08 | 2.25e−09 | 1.82e−07 | 3.64e−09 | |
\(u' \) | 2.85e−07 | 1.40e−07 | 7.32e−07 | 2.70e−07 | ||
64 | u | 3.88e−09 | 3.79e−11 | 1.82e−08 | 9.09e−11 | |
order | 4.00 | 5.89 | 3.33 | 5.32 | ||
\(u' \) | 1.77e−08 | 4.78e−09 | 7.18e−08 | 1.38e−08 | ||
order | 4.01 | 4.87 | 3.35 | 4.30 | ||
100 | 16 | u | 5.57e−06 | 1.55e−06 | 7.17e−06 | 1.33e−06 |
\(u' \) | 3.70e−05 | 3.70e−05 | 3.99e−05 | 3.99e−05 | ||
32 | u | 3.30e−07 | 3.14e−08 | 4.53e−07 | 2.65e−08 | |
\(u' \) | 2.18e−06 | 1.77e−06 | 2.55e−06 | 1.82e−06 | ||
64 | u | 2.03e−08 | 5.59e−10 | 3.36e−08 | 5.33e−10 | |
order | 4.02 | 5.81 | 3.75 | 5.64 | ||
\(u' \) | 1.34e−07 | 6.76e−08 | 1.89e−07 | 7.79e−08 | ||
order | 4.02 | 4.71 | 3.75 | 4.55 |