Explicit Multistep Mixed Finite Element Method for RLW Equation

Table 1

Solitary wave Amp. 0.3 and the errors in 𝐿² and 𝐿^∞ norms for 𝑢, 𝑄₁, 𝑄₂, and 𝑄₃ at 𝑡=20, ℎ=0.125, Δ𝑡=0.1, and −40≤𝑥≤60.

Method	Time	𝑄1	𝑄2	𝑄3	𝐿^2 for 𝑢	𝐿^∞ for 𝑢
Our method	0	3.9797	0.8104	2.5787	0	0
	4	3.9797	0.8104	2.5786	3.6304𝑒−004	5.2892𝑒−005
	8	3.9797	0.8104	2.5786	7.2873𝑒−004	5.8664𝑒−005
	12	3.9797	0.8104	2.5787	1.0817𝑒−003	6.3283𝑒−005
	16	3.9795	0.8104	2.5787	1.4186𝑒−003	6.8001𝑒−005
	20	3.9790	0.8103	2.5785	1.7396𝑒−003	7.7154𝑒−005
[20]	20	3.9800	0.8104	2.5792	1.7569𝑒−003	6.8432𝑒−004
[21]	20	3.9820	0.8087	2.5730	4.688𝑒−003	1.755𝑒−003
[22]	20	3.9905	0.8235	2.6740	2.157𝑒−003	—
[23]	20	3.9616	0.8042	2.5583	0.018𝑒−003	1.566𝑒−003
[24]	20	3.9821	0.8112	2.5813	0.511𝑒−003	0.198𝑒−003