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 | 2.0e–04 | – | – | 3.6e–05 | – | −− | 3.5e–04 | – | – |
1/4 | 7.4e–06 | 3.8e+00 | 4.75 | 5.1e–07 | 2.6e–03 | 6.15 | 1.3e–05 | 2.8e+02 | 4.73 |
1/8 | 3.0e–07 | 2.7e+00 | 4.63 | 7.6e–09 | 2.3e–03 | 6.07 | 5.4e–07 | 1.8e+02 | 4.61 |
1/16 | 1.4e–08 | 1.5e+00 | 4.46 | 1.2e–10 | 2.1e–03 | 6.03 | 2.5e–08 | 9.1e+01 | 4.44 |
1/32 | 6.9e–10 | 8.0e–01 | 4.30 | 1.8e–12 | 2.1e–03 | 6.02 | 1.3e–09 | 4.2e+01 | 4.29 |
1/64 | 3.8e–11 | 4.4e–01 | 4.18 | 2.0e–14 | 8.9e–03 | 6.44 | 7.1e–11 | 2.1e+01 | 4.17 |
1/128 | 2.2e–12 | 2.8e–01 | 4.10 | 3.4e–14 | 1.0e–15 | −0.72 | 4.2e–12 | 1.3e+01 | 4.09 |
1/256 | 1.3e–13 | 2.0e–01 | 4.04 | 1.1e–14 | 1.1e–10 | 1.66 | 2.5e–13 | 8.5e+00 | 4.03 |
1/512 | 7.1e–15 | 8.0e–01 | 4.24 | 2.0e–14 | 5.9e–17 | −0.94 | 1.6e–14 | 8.7e+00 | 4.03 |