Theory and Modern Applications
Table 1 Error comparison of u at different time level with parameters \(h=1/1000\), \(J=320\) and \(\kappa _{0} = 0.1, 0.5\) for Example 1
From: Algorithms for coupled Burgers’ equations by sharing characteristic curves within BSLM
\(\kappa _{0}\) | t | CBSLM3 | SC-SL1 | SL-SC2 | SC-SL3 | CBSLM2 [2] | Kapoor [12] | Lai [14] |
|---|---|---|---|---|---|---|---|---|
0.1 | 1.0 | 1.43e–10 | 4.26e–10 | 1.43e–10 | 1.43e–10 | 2.73e–10 | 2.58e–6 | 5.78e–7 |
2.0 | 2.44e–10 | 2.08e–9 | 2.44e–10 | 2.44e–10 | 4.83e–10 | 2.88e–6 | 1.08e–6 | |
3.0 | 3.18e–10 | 2.83e–9 | 3.18e–10 | 3.18e–10 | 6.49e–10 | 3.18e–6 | 1.49e–6 | |
4.0 | 3.76e–10 | 3.44e–9 | 3.76e–10 | 3.76e–10 | 7.85e–10 | 4.49e–6 | 1.88e–6 | |
5.0 | 4.20e–10 | 3.94e–9 | 4.20e–10 | 4.20e–10 | 8.96e–10 | 3.83e–6 | 2.20e–6 | |
0.5 | 1.0 | 4.55e–7 | 2.05e–6 | 4.55e–7 | 4.55e–7 | 4.83e–6 | 6.27e–7 | 6.75e–4 |
2.0 | 5.53e–7 | 2.20e–6 | 5.53e–7 | 5.53e–7 | 5.24e–6 | 6.70e–7 | 8.17e–4 | |
3.0 | 4.40e–7 | 2.18e–6 | 4.40e–7 | 4.40e–7 | 5.38e–6 | 6.77e–7 | 8.64e–4 | |
4.0 | 4.28e–7 | 2.13e–6 | 4.28e–7 | 4.28e–7 | 5.42e–6 | 6.76e–7 | 8.82e–4 | |
5.0 | 4.16e–7 | 2.07e–6 | 4.16e–7 | 4.16e–7 | 5.43e–6 | 6.73e–7 | 8.91e–4 |