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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