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In this paper, numerical techniques based on the wavelets methods are proposed for the numerical solution of non-linear two-dimensional BBM-BBM system and we compared between them. Two methods used in numerical solutions, are the Haar wavelets and Legendre wavelets methods. In addition, we derived formulas of integrals for Legendre wavelets analytically. Its efficiency is tested by solving an example for which the exact solution is known. The accuracy of the numerical 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. We have found that the Legendre wavelets method is better and closer to the exact solution than the Haar wavelets method.

A Comparative Study of Wavelets Methods for Solving Non-Linear Two-Dimensional Boussinesq System of Type BBM-BBM