Numerical Solution for Non-linear Korteweg-de Vries-Burger's Equation Using the Haar Wavelet Method

Abstract

In this paper, an operational matrix of integrations based on the Haar wavelet method is applied for finding numerical solution of non-linear third-order korteweg-de Vries-Burger's equation, we compared this numerical results with the exact solution. The accuracy of the obtained solutions is quite high even if the number of calculation points is small, by increasing the number of collocation points the error of the solution rapidly decreases as shown by solving an example. We have been reduced the boundary conditions in the solution by using the finite differences method with respect to time. Also we have reduced the order boundary conditions used in the numerical solution by using the boundary condition at x=L instead of the derivatives of order two with respect to space.