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Table 2 Maximum pointwise error at several times for sine-Gordon equation in Example 5.1 with \(N =4\), \(N_{e}=20\), and \(k=0.01\)

From: Legendre spectral element method for solving sine-Gordon equation

Time (second) Max\(\vert {u_{\mathrm{exact}}-u_{\mathrm{LSEM}}} \vert \)
1 3.4862e−03
2 3.7742e−03
3 5.0095e−03
4 5.7173e−03
5 5.7173e−03
6 5.7173e−03
7 1.1208e−02
8 1.5732e−02
9 2.3081e−02
10 3.3925e−02