An efficient numerical method for solving the Korteveg-de Vries equation in a class of discontinuous functions

In this study, an efficient numerical method is proposed and implemented fo r solving the well-known one-dimensional Korteveg-de Vries (KdV) equation i n a class of discontinuous functions. To this end, an auxiliary problem is formulated and it is shown that the solution of the auxiliary problem is th e weak solution of KdV equation. Furthermore, some properties of the soluti on to the auxiliary problem are established. Since no smoothness assumption s are imposed on the unknown function, the numerical method proposed in thi s paper gives better results as compared to the conventional finite differe nce methods. Indeed, several simulations are presented in which the analyti cal solution and the computed numerical solution are in perfect agreement. Further numerical experiments with initial conditions of varying regulariti es are provided. (C) 1999 Elsevier Science Inc. All rights reserved.