Theory and Modern Applications
From: Legendre spectral element method for solving sine-Gordon equation
Time (s) | LSEM | Dehghan and Shokri [18] | Shukla and Tamsir [30] | Mittal and Bhatia [31] | ||||
---|---|---|---|---|---|---|---|---|
\(L_{2}\operatorname{err}\) | \(L_{\infty }\operatorname{err}\) | \(L_{2 }\operatorname{err}\) | \(L_{\infty }\operatorname{err}\) | \(L_{2 }\operatorname{err}\) | \(L_{\infty }\operatorname{err}\) | \(L_{2}\operatorname{err}\) | \(L_{\infty }\operatorname{err}\) | |
0.25 | 2.39e−06 | 4.05e−06 | 3.91e−05 | 5.89e−06 | 2.43e−06 | 5.56e−06 | 1.18e−05 | 2.32e−05 |
0.5 | 6.85e−06 | 7.02e−06 | 1.30e−04 | 2.01e−05 | 5.54e−06 | 7.39e−06 | 4.19e−05 | 4.11e−05 |
0.75 | 6.97e−06 | 7.36e−06 | 2.35e−04 | 3.63e−05 | 6.45e−06 | 7.40e−06 | 7.78e−05 | 1.02e−04 |
1 | 1.07e−05 | 2.23e−05 | 3.27e−04 | 5.07e−05 | 7.84e−06 | 8.75e−06 | 1.30e−04 | 1.64e−04 |