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

RASULOV M., Coskun E.

APPLIED MATHEMATICS AND COMPUTATION, vol.102, pp.139-154, 1999 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 102
  • Publication Date: 1999
  • Doi Number: 10.1016/s0096-3003(98)10022-x
  • Journal Name: APPLIED MATHEMATICS AND COMPUTATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.139-154
  • Keywords: Korteveg-de Vries, solitary waves, travelling waves
  • Karadeniz Technical University Affiliated: Yes

Abstract

In this study, an efficient numerical method is proposed and implemented for solving the well-known one-dimensional Korteveg-de Vries (KdV) equation in 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 the weak solution of KdV equation. Furthermore, some properties of the solution to the auxiliary problem are established. Since no smoothness assumptions are imposed on the unknown function, the numerical method proposed in this paper gives better results as compared to the conventional finite difference methods. Indeed, several simulations are presented in which the analytical solution and the computed numerical solution are in perfect agreement. Further numerical experiments with initial conditions of varying regularities are provided. (C) 1999 Elsevier Science Inc. All rights reserved.