Table 1 IVP ( 47 ), ( 48 ): Convergence of the collocation scheme,
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 | 1.4e–01 | – | – | 9.2e–02 | – | – | 1.4e–01 | – | – |
1/4 | 3.5e–02 | 2.1e+00 | 1.96 | 2.3e–02 | 3.7e–01 | 2.01 | 3.5e–02 | 2.1e+00 | 1.96 |
1/8 | 9.0e–03 | 2.2e+00 | 1.98 | 5.8e–03 | 3.7e–01 | 2.00 | 9.0e–03 | 2.2e+00 | 1.98 |
1/16 | 2.3e–03 | 2.2e+00 | 1.99 | 1.4e–03 | 3.7e–01 | 2.00 | 2.3e–03 | 2.2e+00 | 1.99 |
1/32 | 5.7e–04 | 2.3e+00 | 2.00 | 3.6e–04 | 3.7e–01 | 2.00 | 5.7e–04 | 2.3e+00 | 2.00 |
1/64 | 1.4e–04 | 2.3e+00 | 2.00 | 9.0e–05 | 3.7e–01 | 2.00 | 1.4e–04 | 2.3e+00 | 2.00 |
1/128 | 3.6e–05 | 2.3e+00 | 2.00 | 2.2e–05 | 3.7e–01 | 2.00 | 3.6e–05 | 2.3e+00 | 2.00 |
1/256 | 8.9e–06 | 2.3e+00 | 2.00 | 5.6e–06 | 3.7e–01 | 2.00 | 8.9e–06 | 2.3e+00 | 2.00 |
1/512 | 2.2e–06 | 2.3e+00 | 2.00 | 1.4e–06 | 3.7e–01 | 2.00 | 2.2e–06 | 2.3e+00 | 2.00 |