A High Order IMEX Method for Generalized Korteweg de-Vries Equations

In this paper, we introduce a high order space-time approximation of generalized Korteweg de-Vries equations. More specifically, the method uses continuous $H^1$-conforming finite elements for the spatial approximation and implicit-explicit methods for the temporal approximation. The method is high order in both space, provably stable, and mass-conservative. The scheme is formulated, its properties are proven, and numerical simulations are provided to illustrate the proposed methodology.