From: On linear ODEs with a time singularity of the first kind and unsmooth inhomogeneity
h | Equidistant points | Gaussian points | |||||||
---|---|---|---|---|---|---|---|---|---|
Uniform | Mesh | Uniform | |||||||
| c | p |
| c | p |
| c | p | |
1/2 | 3.7e–03 | – | – | 3.7e–03 | – | – | 7.8e–03 | – | – |
1/4 | 5.1e–04 | 6.4e–01 | 2.87 | 1.6e–04 | 8.4e–02 | 4.50 | 1.2e–03 | 3.6e+00 | 2.73 |
1/8 | 6.6e–05 | 8.1e–01 | 2.96 | 8.1e–06 | 6.7e–02 | 4.34 | 1.5e–04 | 6.4e+00 | 2.93 |
1/16 | 8.3e–06 | 8.8e–01 | 2.99 | 4.4e–07 | 5.1e–02 | 4.21 | 2.0e–05 | 7.6e+00 | 2.98 |
1/32 | 1.0e–06 | 9.0e–01 | 3.00 | 2.5e–08 | 4.0e–02 | 4.12 | 2.5e–06 | 8.1e+00 | 2.99 |
1/64 | 1.3e–07 | 9.1e–01 | 3.00 | 1.5e–09 | 3.3e–02 | 4.06 | 3.1e–07 | 8.4e+00 | 3.00 |
1/128 | 1.6e–08 | 9.2e–01 | 3.00 | 9.3e–11 | 2.9e–02 | 4.03 | 3.8e–08 | 8.5e+00 | 3.00 |
1/256 | 2.0e–09 | 9.2e–01 | 3.00 | 5.7e–12 | 2.7e–02 | 4.02 | 4.8e–09 | 8.5e+00 | 3.00 |
1/512 | 2.6e–10 | 9.2e–01 | 3.00 | 3.5e–13 | 2.8e–02 | 4.03 | 6.0e–10 | 8.5e+00 | 3.00 |