A variation approach to the construction of finite-difference scheme with space-split time derivative for the Korteweg-de Vries equation

The paper presents a variation approach to the construction of finite-difference schemes with space split time derivative (“Cabaret”) for the Korteweg-de Vries (KDV) equation. The test results under different initial distributions are demonstrated. In particular, it is shown that “Cabaret” enjoys the advantage of accurate solution propagation on non-uniform grids over the classical three-layer central differencing (“Cross”).