Numerical Solution and Stability Analysis of Korteweg-de Vries-Burger Equation

Numerical Solution of Korteweg-de Vries-Burger (KdV-B) equation is presented using two finite difference methods ,the explicit scheme and Crank-Nicholson scheme. The accuracy of computed solutions is examined by comparison with analytical solution using example , and it has been found that the explicit scheme is simpler while the Crank-Nicholson is more accurate and has faster convergent . Also , the stability analysis of the two methods by using Fourier (Von Neumann) method has been done and the result was showed that the explicit scheme is stable under the condition and the Crank-Nicholson is unconditionally stable.