Theory and Modern Applications
Table 2 First derivative approximation results with the fourth-order accurate formulae
\(\boldsymbol{\frac{1}{h}}\) | \(\boldsymbol{\Vert v-v_{h}\Vert _{\overline{R}^{h}}}\) | \(\boldsymbol{E_{v}^{m}}\) |
|---|---|---|
\(\frac{1}{8}\) | 1.4993E − 2 | 9.78 |
\(\frac{1}{16}\) | 1.5327E − 3 | 12.93 |
\(\frac{1}{32}\) | 1.1854E − 4 | 14.50 |
\(\frac{1}{64}\) | 8.1771E − 6 | 15.25 |
\(\frac{1}{128}\) | 5.3605E − 7 |  |