Theory and Modern Applications
N | Second order method | Fourth order method | ||||||
---|---|---|---|---|---|---|---|---|
u | \(\boldsymbol {u'} \) | u | \(\boldsymbol {u'} \) | |||||
MAE | RMSE | MAE | RMSE | MAE | RMSE | MAE | RMSE | |
8 | 9.512e−04 | 6.737e−04 | 3.162e−03 | 2.137e−03 | 5.80e−05 | 3.97e−05 | 1.55e−04 | 9.83e−05 |
16 | 2.212e−04 | 7.021e−04 | 1.501e−04 | 4.995e−04 | 3.68e−06 | 2.44e−06 | 1.94e−05 | 7.78e−06 |
32 | 5.410e−05 | 1.729e−04 | 3.576e−05 | 1.206e−04 | 2.36e−07 | 1.54e−07 | 1.67e−06 | 5.65e−07 |
64 | 1.339e−05 | 4.298e−05 | 8.769e−06 | 2.972e−05 | 1.51e−08 | 9.75e−09 | 1.23e−07 | 3.86e−08 |
128 | 3.337e−06 | 1.073e−05 | 2.175e−06 | 7.386e−06 | 9.64e−10 | 6.19e−10 | 8.43e−09 | 2.54e−09 |
256 | 8.335e−07 | 2.682e−06 | 5.421e−07 | 1.841e−06 | 3.66e−11 | 2.45e−11 | 5.37e−10 | 1.68e−10 |
Order | 2.0015 | 2.0001 | 2.0046 | 2.0038 | 4.72 | 4.66 | 3.97 | 3.92 |