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

Table 1

Invariants and error norms for single solitary wave, 𝑐=0.05, ℎ=0.2, 𝑘=0.2, 𝑥₀=40, and 0≤𝑥≤100 (using Crank-Nicolson time discretization).

Time	𝐼1	𝐼2	𝐼3	𝐿2	𝐿∞
Analytical	3.219174	0.465531	8.001323E − 03
0	3.218839	0.4655250	8.007784E − 03	0	0
2	3.218839	0.4655233	8.007697E − 03	0.83581𝐸−04	0.45779𝐸−04
4	3.218854	0.4655215	8.007602E − 03	1.36403𝐸−04	0.45846𝐸−04
6	3.218842	0.4655196	8.007507E − 03	1.92290𝐸−04	0.68890𝐸−04
8	3.218819	0.4655177	8.007410E − 03	2.47879𝐸−04	0.91724𝐸−04
10	3.218794	0.4655159	8.007313E − 03	3.02940𝐸−04	1.13929𝐸−04