The Improved Moving Least-Square Ritz Method for the One-Dimensional Sine-Gordon Equation

Table 2

The comparisons of exact solution with numerical solutions by IEFG and EFG methods with 40 nodes at 𝑡=1 with 𝑑𝑡=0.01 and 𝑑_max=2.2 (Example 2).

Node number	Exact solution	IMLS-Ritz method	EFG method
10	0.0001	0.0001	0.0001
11	0.0004	0.0004	0.0004
12	0.0010	0.0010	0.0010
13	0.0027	0.0027	0.0026
14	0.0073	0.0072	0.0074
15	0.0198	0.0197	0.0196
16	0.0539	0.0536	0.0535
17	0.1464	0.1463	0.1462
18	0.3960	0.3958	0.3956
19	1.0392	1.0396	1.0442
20	2.3000	2.2993	2.2989
21	3.1416	3.1408	3.1406