Theory and Modern Applications
Table 10 Comparison of numerical results of Example 5.2 with Shishkin mesh with \(\varepsilon _{2}=10^{-2}\)
N/Δt | \(\varepsilon _{1}=10^{-4}\) | \(\varepsilon _{1}=10^{-6}\) | ||
|---|---|---|---|---|
Shishkin mesh | Adaptive mesh | Shishkin mesh | Adaptive mesh | |
\(32/\frac{1}{20}\) | 9.1770e − 02 | 1.0625e − 01 | 9.2836e − 02 | 1.7981e − 01 |
0.5076 | 0.6533 | 0.4936 | 0.5783 | |
\(64/\frac{1}{40}\) | 6.4546e − 02 | 6.7754e − 02 | 6.5938e − 02 | 9.7493e − 02 |
0.6481 | 0.7888 | 0.6587 | 0.7454 | |
\(128/\frac{1}{80}\) | 4.1187e − 02 | 3.9103e − 02 | 4.1769e − 02 | 5.3310e − 02 |
0.7238 | 0.8853 | 0.7118 | 0.8093 | |
\(256/\frac{1}{160}\) | 2.4938e − 02 | 2.1170e − 02 | 2.5503e − 02 | 2.8267e − 02 |