Theory and Modern Applications
Table 4 Comparison of the \(L_{2}\operatorname{err}\) and \(L_{\infty }\operatorname{err}\) of Example 5.3 with \(N = 7\), \(N_{e}=30\), and \(k=0.001\) at different time levels
From: Legendre spectral element method for solving sine-Gordon equation
Time (s) | LSEM | Bratsos [40] | Shukla and Tamsir [30] | Mittal and Bhatia [31] | |||
|---|---|---|---|---|---|---|---|
\(L_{2}\operatorname{err}\) | \(L_{\infty }\operatorname{err}\) | \(L_{\infty }\operatorname{err}\) | \(L_{2 }\operatorname{err}\) | \(L_{\infty }\operatorname{err}\) | \(L_{2}\operatorname{err}\) | \(L_{\infty }\operatorname{err}\) | |
1 | 1.024e−06 | 2.321e−06 | 1.276e−04 | 1.868e−09 | 2.318e−09 | 2.564e−05 | 1.818e−05 |
10 | 5.432e−06 | 4.003e−06 | 1.912e−04 | 5.474e−09 | 5.234e−09 | 5.850e−05 | 5.228e−05 |
20 | 2.015e−05 | 1.358e−05 | 2.519e−04 | 9.800e−09 | 5.471e−09 | 1.713e−04 | 9.438e−05 |