EXTENDED B-SPLINE COLLOCATION METHOD FOR KDV-BURGERS EQUATION


Hepson Ö. , Korkmaz A., Dag İ.

TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS, vol.9, no.2, pp.267-278, 2019 (Journal Indexed in ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 9 Issue: 2
  • Publication Date: 2019
  • Title of Journal : TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS
  • Page Numbers: pp.267-278

Abstract

The extended form of the classical polynomial cubic B-spline function is used to set up a collocation method for some initial boundary value problems derived for the Korteweg-de Vries-Burgers equation. Having nonexistence of third order derivatives of the cubic B-splines forces us to reduce the order of the term u(xxx) to give a coupled system of equations. The space discretization of this system is accomplished by the collocation method following the time discretization with Crank-Nicolson method. Two initial boundary value problems, one having analytical solution and the other is set up with a non analytical initial condition, have been simulated by the proposed method.