Table 6 TVP ( 50 ): 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 | 2.2e+00 | – | – | 1.7e+00 | – | – | 1.7e+00 | – | – |
1/4 | 1.5e+00 | 5.4e+00 | 0.51 | 1.2e+00 | 2.4e+00 | 0.51 | 1.2e+00 | 5.4e+00 | 0.51 |
1/8 | 1.1e+00 | 5.3e+00 | 0.50 | 8.5e–01 | 2.4e+00 | 0.50 | 8.5e–01 | 5.3e+00 | 0.50 |
1/16 | 7.5e–01 | 5.3e+00 | 0.50 | 6.0e–01 | 2.4e+00 | 0.50 | 6.0e–01 | 5.2e+00 | 0.50 |
1/32 | 5.3e–01 | 5.2e+00 | 0.50 | 4.2e–01 | 2.4e+00 | 0.50 | 4.2e–01 | 5.2e+00 | 0.50 |
1/64 | 3.8e–01 | 5.2e+00 | 0.50 | 3.0e–01 | 2.4e+00 | 0.50 | 3.0e–01 | 5.2e+00 | 0.50 |
1/128 | 2.7e–01 | 5.2e+00 | 0.50 | 2.1e–01 | 2.4e+00 | 0.50 | 2.1e–01 | 5.2e+00 | 0.50 |
1/256 | 1.9e–01 | 5.2e+00 | 0.50 | 1.5e–01 | 2.4e+00 | 0.50 | 1.5e–01 | 5.2e+00 | 0.50 |
1/512 | 1.3e–01 | 5.2e+00 | 0.50 | 1.1e–01 | 2.4e+00 | 0.50 | 1.1e–01 | 5.2e+00 | 0.50 |