Theory and Modern Applications
From: Algorithms for coupled Burgers’ equations by sharing characteristic curves within BSLM
t | \(\beta _{1} = 10\), \(\beta _{2} = 2\) | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
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 | 3.01e–5 | 2.44e–6 | 0.762 | 3.32e–5 | 3.88e–6 | 0.431 | 4.02e–5 | 2.74e–6 | 0.443 | 1.32e–4 | 3.34e–5 | 0.436 |
2.0 | 4.94e–5 | 4.58e–6 | 1.541 | 5.97e–5 | 6.98e–6 | 0.873 | 6.69e–5 | 5.48e–6 | 0.902 | 3.25e–4 | 5.94e–5 | 0.845 |
3.0 | 6.91e–5 | 6.79e–6 | 2.368 | 8.71e–5 | 1.01e–5 | 1.292 | 9.37e–5 | 8.40e–6 | 1.334 | 5.47e–4 | 8.49e–5 | 1.212 |
5.0 | 1.10e–4 | 1.12e–5 | 3.912 | 1.42e–4 | 1.62e–5 | 2.166 | 1.48e–4 | 1.43e–5 | 2.256 | 1.00e–3 | 1.36e–4 | 1.975 |
7.0 | 1.50e–4 | 1.58e–5 | 5.452 | 1.98e–4 | 2.24e–5 | 3.034 | 2.01e–4 | 2.03e–5 | 3.125 | 1.46e–3 | 1.87e–4 | 2.748 |
9.0 | 1.91e–4 | 2.03e–5 | 7.021 | 2.53e–4 | 2.86e–5 | 3.745 | 2.56e–4 | 2.63e–5 | 4.085 | 1.92e–3 | 2.38e–4 | 3.504 |
t | \(\beta _{1} = 2\), \(\beta _{2} = 10\) | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
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 | 4.90e–6 | 2.40e–5 | 0.772 | 3.88e–6 | 3.32e–5 | 0.447 | 2.74e–6 | 4.02e–5 | 0.451 | 1.44e–5 | 3.15e–4 | 0.432 |
2.0 | 6.81e–6 | 4.38e–5 | 1.568 | 6.98e–6 | 5.97e–5 | 0.865 | 5.48e–6 | 6.69e–5 | 1.006 | 2.11e–5 | 5.52e–4 | 0.815 |
3.0 | 8.69e–6 | 6.37e–5 | 2.346 | 1.01e–5 | 8.71e–5 | 1.306 | 8.40e–6 | 9.37e–5 | 1.329 | 4.26e–5 | 7.83e–4 | 1.218 |
5.0 | 1.28e–5 | 1.04e–4 | 3.917 | 1.62e–5 | 1.42e–4 | 2.167 | 1.43e–5 | 1.48e–4 | 2.260 | 9.04e–5 | 1.24e–3 | 1.961 |
7.0 | 1.71e–5 | 1.45e–4 | 5.441 | 2.24e–5 | 1.98e–4 | 3.057 | 2.03e–5 | 2.01e–4 | 3.231 | 1.41e–4 | 1.70e–3 | 2.708 |
9.0 | 2.15e–5 | 1.86e–4 | 7.001 | 2.86e–5 | 2.53e–4 | 3.884 | 2.63e–5 | 2.56e–4 | 4.173 | 1.91e–4 | 2.16e–3 | 3.472 |