Theory and Modern Applications
Table 4 Accuracies in solution values with quasi-variable meshes in Example 5.3
L  + 1 | \(\boldsymbol {\tilde{\alpha}}\) | \(\boldsymbol {\tilde{\beta}}\) | \(\boldsymbol {\mathcal{E}_{\infty}}\) | \(\boldsymbol {\mathcal{E}_{2}}\) | \(\boldsymbol {\Theta_{\infty}}\) | \(\boldsymbol {\Theta_{2}}\) |
|---|---|---|---|---|---|---|
\(R_{e} =1\) | Â | Â | Â | Â | Â | Â |
4 | 6.75 | 1.15 | 1.18e−02 | 9.94e−03 | – | – |
8 | 0.70 | 0.60 | 1.08e−03 | 4.41e−04 | 4.1 | 4.5 |
16 | 0.12 | 0.10 | 8.65e−05 | 2.05e−05 | 3.6 | 4.4 |
\(R_{e} =10\) | Â | Â | Â | Â | Â | Â |
4 | 6.75 | 1.15 | 1.77e−02 | 9.74e−03 | – | – |
8 | 0.70 | 0.60 | 1.08e−03 | 4.41e−04 | 4.0 | 4.5 |
16 | 0.12 | 0.10 | 8.65e−05 | 2.05e−05 | 3.6 | 4.4 |
\(R_{e} = 10^{3}\) | Â | Â | Â | Â | Â | Â |
4 | 6.75 | 1.15 | 3.24e−02 | 2.38e−02 | – | – |
8 | 0.70 | 0.60 | 1.08e−03 | 4.41e−04 | 4.9 | 5.8 |
16 | 0.12 | 0.10 | 8.55e−05 | 2.02e−05 | 3.7 | 4.4 |
\(R_{e} = 10^{4}\) | Â | Â | Â | Â | Â | Â |
4 | 6.75 | 1.15 | 1.36e−02 | 8.63e−03 | – | – |
8 | 0.70 | 0.60 | 1.08e−03 | 4.41e−04 | 3.7 | 4.3 |
16 | 0.12 | 0.10 | 7.57e−05 | 1.86e−05 | 3.8 | 4.6 |