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

Table 1

The comparisons of exact solution with numerical solutions by IEFG and EFG methods with 41 nodes at 𝑡=0.1 with 𝑑𝑡=0.001 and 𝑑_max=3.0 (Example 1).

Node number	Exact solution	IMLS-Ritz method	EFG method
21	0.1488	0.1479	0.1473
22	0.2939	0.2918	0.2909
23	0.4318	0.4297	0.4275
24	0.5590	0.5583	0.5536
25	0.6725	0.6732	0.6661
26	0.7694	0.7687	0.7653
27	0.8474	0.8471	0.8399
28	0.9045	0.9032	0.8989
29	0.9393	0.9389	0.9380
30	0.8474	0.8478	0.8487
31	0.7694	0.7685	0.7625
32	0.6725	0.6732	0.6753