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 | 2.2e+00 | – | – | 1.5e–01 | – | – | 1.5e–01 | – | – |
1/4 | 2.8e–01 | 1.1e+03 | 2.98 | 3.7e–03 | 5.7e+00 | 5.29 | 4.1e–03 | 4.5e+05 | 5.18 |
1/8 | 2.1e–02 | 8.2e+03 | 3.71 | 8.3e–05 | 7.5e+00 | 5.49 | 8.3e–05 | 2.1e+06 | 5.62 |
1/16 | 1.4e–03 | 1.7e+04 | 3.93 | 5.2e–06 | 3.4e–01 | 4.00 | 5.2e–06 | 2.1e+03 | 4.00 |
1/32 | 8.8e–05 | 2.2e+04 | 3.98 | 3.3e–07 | 3.4e–01 | 4.00 | 3.3e–07 | 2.1e+03 | 4.00 |
1/64 | 5.5e–06 | 2.3e+04 | 4.00 | 2.0e–08 | 3.4e–01 | 4.00 | 2.0e–08 | 2.1e+03 | 4.00 |
1/128 | 3.5e–07 | 2.4e+04 | 4.00 | 1.3e–09 | 3.4e–01 | 4.00 | 1.3e–09 | 2.1e+03 | 4.00 |
1/256 | 2.2e–08 | 2.4e+04 | 4.00 | 8.0e–11 | 3.3e–01 | 3.99 | 8.0e–11 | 2.0e+03 | 3.99 |
1/512 | 1.4e–09 | 2.4e+04 | 4.00 | 7.0e–12 | 2.2e–02 | 3.50 | 7.0e–12 | 4.6e+01 | 3.50 |