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

Table 2

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

Time	𝐼1	𝐼2	𝐼3	𝐿2	𝐿∞
Analytical	3.219174	0.465531	8.001323E − 03
0	3.218839	0.4655250	8.007778E − 03	0	0
2	3.218977	0.4655250	8.007779E − 03	2.613735𝐸−05	4.577868𝐸−05
4	3.219083	0.4655250	8.007780E − 03	3.432730𝐸−05	2.894973𝐸−05
6	3.219165	0.4655250	8.007780E − 03	4.744950𝐸−05	2.214867𝐸−05
8	3.219229	0.4655250	8.007780E − 03	6.052811𝐸−05	2.298029𝐸−05
10	3.219274	0.4655250	8.007780E − 03	7.200630𝐸−05	2.346961𝐸−05