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

Table 4

Table comparing values obtained from the nonstandard numerical scheme (40) 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	0.810462	2.57901	0.00424465	0.00167944
8	3.97995	0.810462	2.57901	0.00839433	0.00337615
12	3.97995	0.810462	2.57901	0.012402	0.00495651
16	3.97995	0.810462	2.57901	0.0162382	0.00639525
20	3.97995	0.810462	2.57901	0.0198962	0.00770612