Theory and Modern Applications
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 |