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101 Numerical Solution for Non-linear Boussinesq System Using the Haar Wavelet Method Ekhlass S. Al-Rawi drekhlass-alrawi@uomosul.edu.iq Ahmed F. Qasim ahmednumerical@yahoo.com College of Computer Sciences and Mathematics University of Mosul, Mosul, Iraq Received on: 02/09/2012 Accepted on: 30/01/2013 ABSTRACT In this paper, an operational matrix of integrations based on the Haar wavelet method is applied for finding the numerical solution of non-linear third-order boussinesq system and the numerical results were compared 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 of 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.