EXTENDED B-SPLINE COLLOCATION METHOD FOR KDV-BURGERS EQUATION
TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS, vol.9, no.2, pp.267-278, 2019 (ESCI, Scopus, TRDizin)
- Publication Type: Article / Article
- Volume: 9 Issue: 2
- Publication Date: 2019
- Journal Name: TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS
- Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, TR DİZİN (ULAKBİM)
- Page Numbers: pp.267-278
- Keywords: KdV-Burgers Equation, Extended cubic B-spline, collocation, motion of waves, NUMERICAL-SOLUTION, WAVE SOLUTIONS, EXPLICIT
- Eskisehir Osmangazi University Affiliated: Yes
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.