Theory and Modern Applications
From: Absolutely stable difference scheme for a general class of singular perturbation problems
\(x_{i}\) | ε = 10−3 | ε = 10−4 | ||||
---|---|---|---|---|---|---|
CFD | ASCD | CFD | ASCD | |||
 | \(\delta_{i}=\frac{4}{\omega|p_{i}|}\) | \(\delta_{i}=\delta_{\mathrm{op}}\) |  | \(\delta_{i}=\frac{4}{\omega|p_{i}|}\) | \(\delta_{i}=\delta_{\mathrm{op}}\) | |
0.00 | 0.0000e + 00 | 0.0000e + 00 | 0.0000e + 00 | 0.0000e + 00 | 0.0000e + 00 | 0.0000e + 00 |
0.01 | 2.5175e − 09 | 2.5175e − 09 | 2.5175e − 09 | 1.2904e − 01 | 1.0226e − 86 | 1.0226e − 86 |
0.02 | 9.4549e − 18 | 9.4549e − 18 | 9.4549e − 18 | 1.5959e − 02 | 5.7090e − 171 | 5.709e − 171 |
0.04 | 4.4278e − 34 | 4.4278e − 34 | 4.4278e − 34 | 2.1328e − 04 | 0.0000e + 00 | 0.0000e + 00 |
0.06 | 4.4806e − 50 | 1.0270e − 49 | 4.4806e − 50 | 2.3489e − 06 | 0.0000e + 00 | 0.0000e + 00 |
0.08 | 6.0646e − 50 | 1.1799e − 64 | 6.0646e − 50 | 2.0935e − 08 | 0.0000e + 00 | 0.0000e + 00 |
0.10 | 6.3669e − 50 | 6.7142e − 79 | 6.3669e − 50 | 1.4785e − 10 | 0.0000e + 00 | 0.0000e + 00 |
0.20 | 8.4790e − 50 | 1.0611e − 139 | 8.4790e − 50 | 2.8784e − 23 | 0.0000e + 00 | 0.0000e + 00 |
0.30 | 1.2675e − 49 | 3.9475e − 183 | 1.2675e − 49 | 2.5563e − 41 | 0.0000e + 00 | 0.0000e + 00 |
0.40 | 2.4911e − 49 | 3.4566e − 209 | 2.4911e − 49 | 2.8289e − 73 | 0.0000e + 00 | 0.0000e + 00 |
0.50 | 2.0204e − 48 | 7.1246e − 218 | 2.0204e − 48 | 8.4555e − 146 | 0.0000e + 00 | 0.0000e + 00 |
0.60 | 2.1996e − 39 | 3.4566e − 209 | 2.1996e − 39 | 1.3376e − 70 | 0.0000e + 00 | 0.0000e + 00 |
0.70 | 4.9323e − 21 | 3.9475e − 183 | 4.9323e − 21 | 2.5837e − 41 | 0.0000e + 00 | 0.0000e + 00 |
0.80 | 3.2994e − 21 | 1.0611e − 139 | 3.2994e − 21 | 2.9094e − 23 | 0.0000e + 00 | 0.0000e + 00 |
0.90 | 2.4776e − 21 | 6.7142e − 79 | 2.4776e − 21 | 1.4785e − 10 | 0.0000e + 00 | 0.0000e + 00 |
0.92 | 2.3599e − 21 | 1.1799e − 64 | 2.3599e − 21 | 2.0935e − 08 | 0.0000e + 00 | 0.0000e + 00 |
0.94 | 2.2529e − 21 | 1.0270e − 49 | 2.2529e − 21 | 2.3489e − 06 | 0.0000e + 00 | 0.0000e + 00 |
0.96 | 2.1552e − 21 | 4.4278e − 34 | 2.1552e − 21 | 2.1328e − 04 | 0.0000e + 00 | 0.0000e + 00 |
0.98 | 9.4528e − 18 | 9.4549e − 18 | 9.4528e − 18 | 1.5959e − 02 | 5.7090e − 171 | 5.709e − 171 |
0.99 | 2.5175e − 09 | 2.5175e − 09 | 2.5175e − 09 | 1.2904e − 01 | 1.0226e − 86 | 1.0226e − 86 |
1.00 | 0.0000e + 00 | 0.0000e + 00 | 0.0000e + 00 | 1.1102e − 16 | 0.0000e + 00 | 0.0000e + 00 |