A Deep Understanding of Non-linear Boussinesq-Burger System of Equation Using Wavelets

This research proposal develops a systematic and efficient mathematical approach of solving the non-linear Boussinesq-Burger's equations system. The primary objective is to develop a scale-3 Haar wavelet-based numerical scheme. In order to authenticate the efficiency, the study investigates a range of numerical problems with different source terms. In order to tackle the intrinsic challenges of nonlinearity of the problems, quasi-linearization method is employed. Explicit analytical expressions for the integrals involved are also derived for both cases under consideration. Validity and accuracy of the proposed scheme are checked by solving problems whose exact solutions are known and by comparing the solutions with special values of parameters. The results show that the Haar scale-3 wavelet method is more efficient with higher accuracy compared to the Haar scale-2 method, as confirmed by comparisons with available studies in the literature.