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Theory and Modern Applications

Table 3 Comparison of \(L_{2 }\operatorname{err}\) and \(L_{\infty }\operatorname{err}\) of Example 5.2 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

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