Theory and Modern Applications
N | Â | Second order | Fourth order | ||
---|---|---|---|---|---|
 | MAE | RMSE | MAE | RMSE | |
10 | u | 7.1411e−06 | 4.8598e−06 | 1.5183e−08 | 1.0322e−08 |
\(u' \) | 2.4886e−05 | 1.6832e−05 | 4.8261e−08 | 3.5393e−08 | |
v | 3.3399e−06 | 2.2408e−06 | 2.0788e−08 | 1.4229e−08 | |
\(v' \) | 1.1264e−05 | 8.1372e−06 | 7.3344e−08 | 4.6608e−08 | |
20 | u | 1.8060e−06 | 1.1822e−06 | 9.4738e−10 | 6.2681e−10 |
\(u'\) | 6.4868e−06 | 4.1284e−06 | 3.0174e−09 | 2.1522e−09 | |
v | 8.5494e−07 | 5.5949e−07 | 1.2768e−09 | 8.4967e−10 | |
\(v' \) | 2.6592e−06 | 1.9574e−06 | 4.7506e−09 | 2.9017e−09 | |
40 | u | 4.5147e−07 | 2.9169e−07 | 5.9265e−11 | 3.8611e−11 |
\(u'\) | 1.6208e−06 | 1.0204e−06 | 1.8898e−10 | 1.3259e−10 | |
v | 2.1498e−07 | 1.3896e−07 | 8.0073e−11 | 5.2627e−11 | |
\(v' \) | 6.7508e−07 | 4.8234e−07 | 3.0237e−10 | 1.8155e−10 | |
Order | u | 2.0046 | 2.0092 | 4.00 | 4.02 |
Order | \(u' \) | 2.0020 | 2.0087 | 4.00 | 4.02 |
Order | v | 2.0253 | 2.0288 | 4.00 | 4.01 |
Order | \(v' \) | 2.0268 | 2.0305 | 3.97 | 4.00 |