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 | 5.4e+00 | – | – | 2.1e+00 | – | – | 1.9e+00 | – | – |
1/4 | 2.3e+00 | 5.2e+01 | 1.26 | 2.3e–01 | 1.8e+01 | 3.17 | 2.2e–01 | 2.2e+03 | 3.14 |
1/8 | 6.8e–01 | 1.7e+02 | 1.73 | 1.7e–02 | 4.2e+01 | 3.76 | 1.6e–02 | 1.3e+04 | 3.74 |
1/16 | 1.8e–01 | 3.1e+02 | 1.93 | 1.1e–03 | 6.1e+01 | 3.94 | 1.1e–03 | 2.6e+04 | 3.93 |
1/32 | 4.5e–02 | 3.8e+02 | 1.98 | 7.0e–05 | 6.9e+01 | 3.98 | 6.8e–05 | 3.3e+04 | 3.98 |
1/64 | 1.1e–02 | 4.1e+02 | 2.00 | 4.4e–06 | 7.2e+01 | 4.00 | 4.3e–06 | 3.5e+04 | 4.00 |
1/128 | 2.8e–03 | 4.2e+02 | 2.00 | 2.7e–07 | 7.3e+01 | 4.00 | 2.7e–07 | 3.6e+04 | 4.00 |
1/256 | 7.1e–04 | 4.2e+02 | 2.00 | 1.7e–08 | 7.3e+01 | 4.00 | 1.7e–08 | 3.6e+04 | 4.00 |
1/512 | 1.8e–04 | 4.2e+02 | 2.00 | 1.1e–09 | 7.4e+01 | 4.00 | 1.0e–09 | 3.6e+04 | 4.00 |