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 | |||
 | \(\delta_{i}=\frac{4}{\omega|p_{i}|}\) | \(\delta_{i}=\delta_{\mathrm{op}}\) |  | \(\delta_{i}=\frac{4}{\omega|p_{i}|}\) | \(\delta_{i}=\delta_{\mathrm{op}}\) | |
0.000 | 3.6835e − 13 | 0.0000e + 00 | 3.6835e − 13 | 1.3312e − 12 | 0.0000e + 00 | 0.0000e + 00 |
0.001 | 3.4477e − 02 | 3.6814e − 01 | 3.4477e − 02 | 6.6658e − 01 | 7.5381e − 04 | 7.5381e − 04 |
0.002 | 2.4176e − 02 | 1.3606e − 01 | 2.4176e − 02 | 4.4436e − 01 | 7.9840e − 04 | 7.9840e − 04 |
0.003 | 1.2725e − 02 | 5.0684e − 02 | 1.2725e − 02 | 2.9624e − 01 | 7.9760e − 04 | 7.9760e − 04 |
0.004 | 5.9580e − 03 | 1.9275e − 02 | 5.9580e − 03 | 1.9749e − 01 | 7.9680e − 04 | 7.9680e − 04 |
0.005 | 2.6175e − 03 | 7.7195e − 03 | 2.6175e − 03 | 1.3166e − 01 | 7.9600e − 04 | 7.9600e − 04 |
0.006 | 1.1048e − 03 | 3.4678e − 03 | 1.1048e − 03 | 8.7774e − 02 | 7.9520e − 04 | 7.9520e − 04 |
0.007 | 4.5373e − 04 | 1.9031e − 03 | 4.5373e − 04 | 5.8516e − 02 | 7.9440e − 04 | 7.9440e − 04 |
0.008 | 1.8268e − 04 | 1.3268e − 03 | 1.8268e − 04 | 3.9011e − 02 | 7.9360e − 04 | 7.9360e − 04 |
0.009 | 7.2459e − 05 | 1.1142e − 03 | 7.2459e − 05 | 2.6007e − 02 | 7.9280e − 04 | 7.9280e − 04 |
0.010 | 2.8408e − 05 | 1.0353e − 03 | 2.8408e − 05 | 1.7338e − 02 | 7.9200e − 04 | 7.9200e − 04 |
0.020 | 1.7708e − 09 | 9.8000e − 04 | 1.7708e − 09 | 3.0067e − 04 | 7.8400e − 04 | 7.8400e − 04 |
0.050 | 5.5511e − 16 | 9.5000e − 04 | 5.5511e − 16 | 1.5680e − 09 | 7.6000e − 04 | 7.6000e − 04 |
0.100 | 4.4409e − 16 | 9.0000e − 04 | 4.4409e − 16 | 8.8818e − 16 | 7.2000e − 04 | 7.2000e − 04 |
0.300 | 2.2204e − 16 | 7.0000e − 04 | 2.2204e − 16 | 3.3307e − 16 | 5.6000e − 04 | 5.6000e − 04 |
0.500 | 2.2204e − 16 | 5.0000e − 04 | 2.2204e − 16 | 3.3307e − 16 | 4.0000e − 04 | 4.0000e − 04 |
1.000 | 0.0000e + 00 | 0.0000e + 00 | 0.0000e + 00 | 0.0000e + 00 | 0.0000e + 00 | 0.0000e + 00 |