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

Table 3

Invariants and error norms for single solitary wave, 𝑐=0.05, ℎ=0.2, 𝑘=0.2, 𝑥₀=40, 0≤𝑥≤100, and time = 10.

Method	𝐼1	𝐼2	𝐼3	𝐿2	𝐿∞
Analytical	3.219174	0.465531	8.001323E − 03
Our scheme in (22)	3.218794	0.4655160	8.007313E − 03	3.02940𝐸−04	1.13929𝐸−04
Our scheme in (27)	3.219274	0.4655250	8.007780E − 03	0.720063𝐸−04	0.234696𝐸−04
Quadratic [28]	3.215653	0.4655665	8.004883E − 03	1.99288𝐸−04	4.81156𝐸−04
Cubic [28]	3.215189	0.4655136	7.999173E − 03	4.53811𝐸−04	6.25887𝐸−04