We proposed a hybrid compact-CIP scheme to solve the Korteweg-de Vries equation. The algorithm is based on classical constrained interpolation profile (CIP) method, which is coupled with high-order compact scheme for the third derivatives in Korteweg-de Vries equation. Several numerical examples are presented to confirm the high resolution of the proposed scheme.
YuFeng Shi. Biao XU. Yan Guo. "A Compact-Type CIP Method for General Korteweg-de Vries Equation." Abstr. Appl. Anal. 2014 1 - 9, 2014. https://doi.org/10.1155/2014/640194