The Spectral Method for Solving Sine-Gordon Equation Using a New Orthogonal Polynomial

Table 3

The 𝐿₂ error norm for different values of 𝑁 of Experiment 2.

T	𝑁=4	𝑁=8	𝑁=16
0.1	5.02×10^−6	9.11×10^−9	9.56×10^−15
0.2	5.37×10^−5	1.00×10^−8	1.35×10^−13
0.3	2.05×10^−4	3.67×10^−7	2.22×10^−13
0.4	5.00×10^−4	8.37×10^−6	9.10×10^−13
0.5	9.46×10^−4	1.29×10^−6	3.43×10^−12
0.6	1.50×10^−3	1.52×10^−6	1.75×10^−11
0.7	2.10×10^−3	1.58×10^−6	1.29×10^−10
0.8	2.65×10^−3	1.65×10^−6	8.08×10^−10
0.9	3.08×10^−3	1.94×10^−6	4.94×10^−9
1.0	3.37×10^−3	2.13×10^−6	2.26×10^−8