A Compact-Type CIP Method for General Korteweg-de Vries Equation

Table 1

Numerical errors and orders of CIP-HOC method for the KdV equation (29).

𝑁	𝐿∞ error	𝐿∞ order	𝐿2 error	𝐿2 order	𝐼1	𝐼2	𝐼3	Cost(s)
20	5.72𝐸−03		9.94𝐸−03		1.9968246	0.6627258	0.5745942	6.25𝐸−05
40	1.32𝐸−03	2.12	1.89𝐸−03	2.39	1.9996543	0.6663460	0.5774709	2.50𝐸−04
80	2.11𝐸−04	2.65	2.85𝐸−04	2.73	1.9999840	0.6666518	0.5777566	2.50𝐸−03
160	2.77𝐸−05	2.93	3.61𝐸−05	2.98	1.9999984	0.6666662	0.5777761	3.13𝐸−02
320	3.49𝐸−06	2.99	4.54𝐸−06	2.99	1.9999988	0.6666667	0.5777776	6.09𝐸−01