EXTENDED B-SPLINE COLLOCATION METHOD FOR KDV-BURGERS EQUATION

O. E. HEPSON1, A. KORKMAZ2, I. DAG3

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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 uxxx 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.

Keywords

KdV-Burgers Equation; Extended cubic B-spline; collocation; motion of waves.