Theory and Modern Applications
Table 2 The numerical errors and convergence orders in temporal direction (\(h=1/80\))
α | N | ID scheme | ASC-N scheme | ||||
|---|---|---|---|---|---|---|---|
\(L^{2}_{h,\tau }\) | order 1 | CPU (times) | \(L^{2}_{h,\tau }\) | order 1 | CPU (times) | ||
0.8 | 400 | 1.553456e–4 | — | 0.592518 | 1.615210e–4 | — | 0.121606 |
800 | 6.820719e–5 | 1.187486 | 1.572824 | 6.961018e–5 | 1.214352 | 0.272843 | |
1600 | 2.980843e–5 | 1.194203 | 4.995801 | 3.013909e–5 | 1.207662 | 0.757238 | |
3200 | 1.299478e–5 | 1.197787 | 17.68847 | 1.307457e–5 | 1.204872 | 2.459121 | |
6400 | 5.657158e–6 | 1.199783 | 67.09086 | 5.676690e–6 | 1.203642 | 8.867395 | |
0.5 | 400 | 3.023084e–5 | — | 0.614962 | 3.901743e–5 | — | 0.133529 |
800 | 1.072534e–5 | 1.494996 | 1.557829 | 1.244259e–5 | 1.648831 | 0.260445 | |
1600 | 3.788676e–6 | 1.501258 | 4.963961 | 4.138894e–6 | 1.587970 | 0.741085 | |
3200 | 1.332788e–6 | 1.507246 | 17.56794 | 1.406616e–6 | 1.557016 | 2.419346 | |
6400 | 4.666755e–7 | 1.513955 | 66.60791 | 4.827127e–7 | 1.542992 | 8.741754 | |
0.4 | 400 | 1.399030e–5 | — | 0.621470 | 2.705434e–5 | — | 0.136365 |
800 | 4.601493e–6 | 1.604253 | 1.568314 | 7.015947e–6 | 1.947150 | 0.266416 | |
1600 | 1.501415e–6 | 1.615778 | 4.983283 | 1.980694e–6 | 1.824631 | 0.761807 | |
3200 | 4.849224e–7 | 1.630497 | 17.93907 | 5.825449e–7 | 1.765565 | 2.535364 | |
6400 | 1.543647e–7 | 1.651411 | 67.22779 | 1.746222e–7 | 1.738132 | 9.100791 | |