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

Table 4

Invariants and error norms for single solitary wave, 𝑐=0.3, ℎ=0.1, 𝑘=0.01, 𝑥₀=40, and 0≤𝑥≤100 (using Crank-Nicolson 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	1.42310𝐸−04	0.45779𝐸−04
4	3.581966	1.344973	0.1538262	2.65355𝐸−04	1.53988𝐸−04
6	3.581966	1.344973	0.1538261	3.74673𝐸−04	2.00152𝐸−04
8	3.581966	1.344972	0.1538260	4.77620𝐸−04	2.42916𝐸−04
10	3.581966	1.344972	0.1538260	5.77512𝐸−04	2.84373𝐸−04
[27]	3.58197	1.34508	0.153723	4.02927𝐸−04	2.06732𝐸−04