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

Table 3

The comparisons of exact solution with numerical solutions by IEFG and EFG methods with 81 nodes at 𝑡=1 with 𝑑𝑡=0.001 and 𝑑_max=2.7 (Example 3).

Node number	Exact solution	IMLS-Ritz method	EFG method
30	0.0039	0.0037	0.0036
31	0.0070	0.0068	0.0059
32	0.0124	0.0125	0.0131
33	0.0222	0.0231	0.0229
34	0.0395	0.0402	0.0423
35	0.0703	0.0710	0.0722
36	0.1252	0.1251	0.1253
37	0.2228	0.2225	0.2231
38	0.3960	0.3948	0.3952
39	0.7004	0.6978	0.6988
40	1.2212	1.2209	1.2301
41	2.0462	2.0471	2.0483