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

Table 4

Invariant values for a single solitary wave: amplitude = 0.3, 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	3.97990	0.810461	2.57901	3.97992	0.810462	2.57900
4	3.97995	0.810461	2.57901	3.97995	0.810276	2.57839
8	3.97997	0.810461	2.57901	3.97997	0.810276	2.57839
12	3.97998	0.810461	2.57901	3.97998	0.810276	2.57839
16	3.97999	0.810461	2.57901	3.97998	0.810276	2.57839
20	3.97996	0.810461	2.57901	3.97996	0.810276	2.57839