A Modified Equation Approach to Selecting a Nonstandard Finite Difference Scheme Applied to the Regularized Long Wave Equation

Table 3

Table comparing values obtained from the implicit scheme (35) to the single solitary wave solution (8) for 𝑥₀=0 and 𝑣=0.1, for 𝑥∈[−50,70], and taking 𝑛=5000 and Δ𝑡=0.0001.

Time	𝐼1	𝐼2	𝐼3	𝐿2×10^3	𝐿∞×10^3
0	3.97995	0.810462	2.57901	0.00000	0.00000
4	3.97995	0.810463	2.57901	0.0044822	0.00190039
8	3.97995	0.810464	2.57901	0.00884828	0.00377625
12	3.97995	0.810466	2.57902	0.0130448	0.00550027
16	3.97995	0.810467	2.57902	0.0170392	0.00705772
20	3.97995	0.810468	2.57903	0.0208237	0.00846861