Theory and Modern Applications
From: Algorithms for coupled Burgers’ equations by sharing characteristic curves within BSLM
t | ν = 0.1 | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
CBSLM3 | SC-SL3 | SC-SL2 | CBSLM2 [2] | |||||||||
\(\mathrm{E}_{\infty}(u)\) | \(\mathrm{E}_{\infty}(v)\) | CPU | \(\mathrm{E}_{\infty}(u)\) | \(\mathrm{E}_{\infty}(v)\) | CPU | \(\mathrm{E}_{\infty}(u)\) | \(\mathrm{E}_{\infty}(v)\) | CPU | \(\mathrm{E}_{\infty}(u)\) | \(\mathrm{E}_{\infty}(v)\) | CPU | |
1.0 | 1.34e–7 | 3.75e–8 | 40.109 | 1.34e–7 | 5.70e–8 | 21.290 | 2.29e–7 | 1.09e–7 | 21.392 | 2.83e–6 | 1.20e–6 | 19.923 |
2.0 | 1.41e–7 | 4.00e–8 | 79.928 | 1.40e–7 | 6.20e–8 | 42.555 | 3.16e–7 | 1.45e–7 | 43.115 | 4.04e–6 | 1.95e–6 | 39.938 |
3.0 | 1.49e–7 | 4.23e–8 | 120.273 | 1.46e–7 | 6.54e–8 | 63.541 | 4.03e–7 | 1.80e–7 | 64.403 | 5.33e–6 | 2.68e–6 | 59.636 |
5.0 | 1.64e–7 | 4.69e–8 | 199.060 | 1.57e–7 | 7.10e–8 | 100.729 | 5.82e–7 | 2.46e–7 | 107.506 | 8.05e–6 | 4.12e–6 | 99.475 |
7.0 | 1.78e–7 | 5.14e–8 | 278.519 | 1.69e–7 | 7.60e–8 | 147.976 | 7.61e–7 | 3.11e–7 | 148.760 | 1.09e–5 | 5.52e–6 | 138.652 |
9.0 | 1.93e–7 | 5.59e–8 | 358.730 | 1.80e–7 | 8.07e–8 | 191.171 | 9.41e–7 | 3.75e–7 | 192.853 | 1.37e–5 | 6.91e–6 | 179.023 |
t | ν = 0.01 | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
CBSLM3 | SC-SL3 | SC-SL2 | CBSLM2 [2] | |||||||||
\(\mathrm{E}_{\infty}(u)\) | \(\mathrm{E}_{\infty}(v)\) | CPU | \(\mathrm{E}_{\infty}(u)\) | \(\mathrm{E}_{\infty}(v)\) | CPU | \(\mathrm{E}_{\infty}(u)\) | \(\mathrm{E}_{\infty}(v)\) | CPU | \(\mathrm{E}_{\infty}(u)\) | \(\mathrm{E}_{\infty}(v)\) | CPU | |
1.0 | 2.32e–3 | 4.61e–4 | 39.790 | 2.29e–3 | 6.95e–4 | 21.367 | 4.72e–3 | 1.35e–3 | 26.467 | 1.64e–2 | 3.44e–3 | 20.147 |
2.0 | 2.83e–3 | 5.10e–4 | 79.383 | 2.82e–3 | 8.50e–4 | 42.610 | 7.78e–3 | 2.33e–3 | 53.094 | 2.93e–2 | 6.24e–3 | 39.745 |
3.0 | 3.34e–3 | 5.60e–4 | 123.809 | 3.34e–3 | 1.00e–3 | 64.103 | 1.17e–2 | 3.38e–3 | 79.825 | 4.21e–2 | 9.04e–3 | 60.158 |
5.0 | 4.36e–3 | 6.60e–4 | 200.306 | 4.40e–3 | 1.31e–3 | 102.442 | 1.97e–2 | 5.50e–3 | 132.757 | 6.76e–2 | 1.47e–2 | 99.885 |
7.0 | 5.37e–3 | 7.59e–4 | 274.728 | 5.44e–3 | 1.61e–3 | 145.512 | 2.76e–2 | 7.61e–3 | 185.927 | 9.25e–2 | 2.03e–2 | 140.867 |
9.0 | 6.39e–3 | 8.57e–4 | 362.107 | 6.49e–3 | 1.92e–3 | 191.648 | 3.56e–2 | 9.71e–3 | 192.787 | 1.17e–1 | 2.58e–2 | 178.660 |