Extended B-Spline Collocation Method For KdV-Burgers Equation
This work provides a numerical method for solving the KdV-Burgers equation, which is relevant for researchers in computational fluid dynamics and nonlinear wave phenomena.
The authors developed an extended B-spline collocation method for the KdV-Burgers equation, reducing the third-order derivative term to a coupled system. The method was tested on two problems, one with an analytical solution, achieving accurate numerical results.
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.