This research proposal introduces an efficient mathematical scheme for solving the non-linear Boussinesq-Burger's system of equations. The scheme leverages Haar scale-3 wavelets for its development. The study also involves the exploration of numerical problems featuring various source terms. To address the challenges posed by nonlinearity, a quasi-linearization technique is employed. Additionally, analytic formulas for integrals are derived for both cases. By tackling problems with known exact solutions and considering the exact solution with parameter values, the suggested scheme's accuracy is evaluated. The findings indicate that the efficiency of Haar scale-3 surpasses that of Haar scale-2, as confirmed by a comparison with existing literature.