Theory and Modern Applications
Table 3 Numerical results for \(\pmb{p=1}\)
From: Multilevel anti-derivative wavelets with augmentation for nonlinear boundary value problems
n | \(\dim S_{n}\) | \(\Vert u-u_{n} \Vert \) | \(\text{Time}_{n}\) | \(\Vert u-u_{1,n-1} \Vert \) | \(\text{Time}_{1,n-1}\) | \(\Vert u-u_{2,n-2} \Vert \) | \(\text{Time}_{2,n-2}\) | \(\Vert u-u_{3,n-3} \Vert \) | \(\text{Time}_{3,n-3}\) |
|---|---|---|---|---|---|---|---|---|---|
1 | 3 | 2.3184e+0 | 3.5800e–2 | 2.3962e+0 | 8.3000e–3 |  |  |  |  |
2 | 7 | 9.8550e–1 | 2.3140e–1 | 1.3037e+0 | 3.7700e–1 | 1.0073e+0 | 1.7500e–2 |  |  |
3 | 15 | 4.3358e–1 | 1.7408e+0 | 4.5435e–1 | 6.2230e–1 | 4.3987e–1 | 4.4840e–1 | 4.3458e–1 | 5.6600e–2 |
4 | 31 | 2.0971e–1 | 1.6873e+1 | 2.1642e–1 | 7.3150e–1 | 2.1044e–1 | 7.3400e–1 | 2.0832e–1 | 4.9160e–1 |
5 | 63 | 1.1300e–1 | 1.3638e+2 | 1.1440e–1 | 8.4620e–1 | 1.1187e–1 | 8.3810e–1 | 1.1097e–1 | 8.2520e–1 |