The Method of Lines Solution of the Regularized Long-Wave Equation Using Runge-Kutta Time Discretization Method

Table 7

Invariant values for a single solitary wave: amplitude = 0.09, Δ𝑥=0.125,Δ𝑡=0.1 and over the region −40≤𝑥≤60.

𝑡	Present method			Cubic spline collocation method [8]
	𝐶1	𝐶2	𝐶3	𝐶1	𝐶2	𝐶3
0	2.10700	0.127302	0.38806	2.10702	0.127302	0.388804
4	2.10836	0.127302	0.38807	2.10838	0.127294	0.388781
8	2.10927	0.127302	0.38807	2.10928	0.127294	0.388782
12	2.10980	0.127302	0.38807	2.10981	0.127294	0.388782
16	2.10981	0.127302	0.38807	2.10981	0.127294	0.388782
20	2.10899	0.127302	0.38806	2.10900	0.127294	0.388781