Title: Extended B-Spline Collocation Method For KdV-Burgers Equation,
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.