Theory and Modern Applications
Table 3 Accuracies in solution values with uniform 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 | 0 | 0 | 4.15e+01 | 2.32e+01 | – | – |
8 | 0 | 0 | 3.63e+01 | 1.78e+01 | 0.1 | 0.3 |
16 | 0 | 0 | 6.10e−01 | 2.66e−01 | 5.9 | 6.1 |
\(R_{e} =10\) | Â | Â | Â | Â | Â | Â |
4 | 0 | 0 | 3.00e+01 | 1.19e+01 | – | – |
8 | 0 | 0 | 2.62e+01 | 1.17e+01 | 0.2 | 0.03 |
16 | 0 | 0 | 1.03e−00 | 4.63e−01 | 4.7 | 4.7 |
\(R_{e} = 10^{3}\) | Â | Â | Â | Â | Â | Â |
4 | 0 | 0 | 1.84e+01 | 8.95e+00 | – | – |
8 | 0 | 0 | 1.16e+01 | 4.85e+00 | 0.6 | 0.8 |
16 | 0 | 0 | 4.95e+00 | 8.42e−01 | 1.2 | 2.5 |
\(R_{e} = 10^{4}\) | Â | Â | Â | Â | Â | Â |
4 | 0 | 0 | 1.80e+01 | 8.84e+00 | – | – |
8 | 0 | 0 | 1.14e+01 | 4.75e+00 | 0.6 | 0.8 |
16 | 0 | 0 | 4.86e+00 | 8.43e−01 | 1.2 | 2.5 |