Table 8 Comprasions of result for the single solitary wave with \(\mu =1,x\in \left[ 0,100\right] \)
From: A numerical investigation of the GRLW equation using lumped Galerkin approach with cubic B-spline
Methods | \({L_{2}}\times 10^{3}\) | \({L_{\infty}}\times 10^{3}\) | \({I_{1}}\) | \( {I_{2}}\) | \({I_{3}}\) | |
|---|---|---|---|---|---|---|
\(p=2\) | CBSC-CN (Gardner et al. 1995) | 16.3900 | 9.2400 | 4.4420 | 3.2990 | 1.4130 |
\(c=1\) | CBSC+PA-CN (Gardner et al. 1995) | 20.3000 | 11.2000 | 4.4400 | 3.2960 | 1.4110 |
\(h=0.2\) | CBSC (Khalifa et al. 2008) | 9.3019 | 5.4371 | 4.4428 | 3.2998 | 1.4142 |
\({\Delta{t}}=0.025\) | MFC (Ali 2009) | 3.9140 | 2.0190 | 4.4428 | 3.2997 | 1.4141 |
\(t=10\) | QBSPG (Roshan 2012) | 3.0053 | 1.6874 | 4.4428 | 3.2998 | 1.4141 |
QBSC (Karakoç et al. 2013) | 2.4155 | 1.0797 | 4.4431 | 3.3003 | 1.4146 | |
EBSC (Mohammadi 2015) | 2.3909 | 1.0647 | 4.4428 | 3.2998 | 1.4142 | |
Ours-CBSG | 2.4175 | 1.0809 | 4.4431 | 3.3003 | 1.4146 | |
QBSPG (Roshan 2012) | ||||||
\(p=3\) | t = 1 | 0.0101 | 0.0080 | 3.6775 | 1.5657 | 0.2268 |
\(c=0.3\) | t = 5 | 0.0409 | 0.0238 | 3.6775 | 1.5657 | 0.2268 |
\(h=0.1\) | t = 10 | 0.0719 | 0.0377 | 3.6775 | 1.5657 | 0.2268 |
Ours-CBSG | ||||||
\({\Delta{t}}=0.01\) | t = 1 | 0.0706 | 0.0514 | 3.6776 | 1.5657 | 0.2268 |
t = 5 | 0.1702 | 0.0876 | 3.6776 | 1.5657 | 0.2268 | |
t = 10 | 0.1913 | 0.0779 | 3.6776 | 1.5657 | 0.2268 | |
QBSPG (Roshan 2012) | ||||||
\(p=4\) | t = 1 | 0.0158 | 0.0138 | 3.7592 | 1.7299 | 0.2894 |
\(c=0.3\) | t = 5 | 0.0542 | 0.0382 | 3.7592 | 1.7299 | 0.2894 |
\(h=0.1\) | t = 10 | 0.1225 | 0.0662 | 3.7592 | 1.7299 | 0.2894 |
Ours-CBSG | ||||||
\({\Delta{t}}=0.01\) | t = 1 | 0.1222 | 0.0983 | 3.7592 | 1.7300 | 0.2894 |
t = 5 | 0.2591 | 0.1357 | 3.7592 | 1.7300 | 0.2894 | |
t = 10 | 0.3089 | 0.1444 | 3.7592 | 1.7300 | 0.2894 | |