Theory and Modern Applications
Table 4 First derivative approximation results with the fifth-order accurate formulae
\(\boldsymbol{\frac{1}{h}}\) | \(\boldsymbol{\Vert v-v_{h}\Vert _{\overline{R}^{h}}}\) | \(\boldsymbol{E_{v}^{m}}\) |
|---|---|---|
\(\frac{1}{8}\) | 2.0469E − 3 | 22.08 |
\(\frac{1}{16}\) | 9.2725E − 5 | 27.35 |
\(\frac{1}{32}\) | 3.3903E − 6 | 29.78 |
\(\frac{1}{64}\) | 1.1382E − 7 | 30.91 |
\(\frac{1}{128}\) | 3.6823E − 9 |  |