A Galerkin Finite Element Method for Numerical Solutions of the Modified Regularized Long Wave Equation

Table 5

Invariants and error norms for single solitary wave, 𝑐=0.3, ℎ=0.1, 𝑘=0.01, 𝑥₀=40, and 0≤𝑥≤100 (using Runge-Kutta time discretization).

Time	𝐼1	𝐼2	𝐼3	𝐿2	𝐿∞
Analytical	3.581967	1.345076	0.1537230
0	3.581967	1.344973	0.1538264	0	0
2	3.581967	1.344973	0.1538263	1.396685𝐸−04	0.920780𝐸−04
4	3.581967	1.344973	0.1538262	2.592545𝐸−04	1.512530𝐸−04
6	3.581967	1.344973	0.1538262	3.647701𝐸−04	1.956752𝐸−04
8	3.581967	1.344973	0.1538262	4.638980𝐸−04	2.368004𝐸−04
10	3.581967	1.344973	0.1538262	5.600205𝐸−04	2.766940𝐸−04
[27]	3.58197	1.34508	0.153723	4.02927𝐸−04	2.06732𝐸−04