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Theory and Modern Applications

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