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 | 3.2e–03 | – | – | 6.2e–04 | – | – | 1.2e–03 | – | – |
1/4 | 1.1e–03 | 1.0e–01 | 1.49 | 2.2e–04 | 1.7e–03 | 1.50 | 4.4e–04 | 1.9e–01 | 1.50 |
1/8 | 4.1e–04 | 1.0e–01 | 1.50 | 7.7e–05 | 1.7e–03 | 1.50 | 1.6e–04 | 1.9e–01 | 1.50 |
1/16 | 1.4e–04 | 1.0e–01 | 1.50 | 2.7e–05 | 1.7e–03 | 1.50 | 5.5e–05 | 1.9e–01 | 1.50 |
1/32 | 5.1e–05 | 1.0e–01 | 1.50 | 9.6e–06 | 1.7e–03 | 1.50 | 1.9e–05 | 1.9e–01 | 1.50 |
1/64 | 1.8e–05 | 1.0e–01 | 1.50 | 3.4e–06 | 1.7e–03 | 1.50 | 2.4e–04 | 3.6e–15 | −3.65 |
1/128 | 8.0e–05 | 7.4e–11 | −2.15 | 1.2e–06 | 1.7e–03 | 1.50 | 4.9e–03 | 3.4e–17 | −4.34 |
1/356 | 7.9e–04 | 4.0e–14 | −3.31 | 4.3e–07 | 1.7e–03 | 1.50 | 1.0e–01 | 2.1e–17 | −4.40 |
1/512 | 2.5e–02 | 2.5e–19 | −4.99 | 1.5e–07 | 1.7e–03 | 1.50 | 4.8e–01 | 1.5e–09 | −2.20 |