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Table 1 Numerical results for sine-Gordon equation Example 5.1 with \(N{_{e}}=20\) and \(T=1\)

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

  k = 0.1 k = 0.01
N \(L_{2}\operatorname{err}\) \(L_{\infty }\operatorname{err}\) RMSerr \({L_{2}}\operatorname{err}\) \(L_{\infty }\operatorname{err}\) RMSerr
1 2.4093e−01 1.6930e−01 1.1473e−02 2.4629e−01 1.7297e−01 1.1728e−02
2 1.2518e−01 7.9776e−02 3.0531e−03 1.3130e−01 8.3774e−02 3.2024e−03
3 2.2023e−02 9.9553e−03 3.6104e−04 2.4071e−02 1.0268e−02 3.9460e−04
4 3.9778e−03 1.9421e−03 4.9109e−05 6.4771e−03 3.4862e−03 7.9964e−05
5 3.5862e−03 1.3858e−03 3.5507e−05 1.0154e−03 5.3085e−04 1.0053e−05
6 3.5050e−03 1.3304e−03 2.8967e−05 3.5765e−04 1.5567e−04 2.9558e−06
7 3.7733e−03 1.2734e−03 2.6761e−05 3.5359e−04 1.2447e−04 2.5078e−06