Abstract
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.
Highlights
Boussinesq developed the original formulation of the governing equations for a free surface flow, which included the effects of surface waves, but in which the verticalEkhlass S
AL-Rawi and Qasem [2] found the numerical solution for non-linear Murray equation by the operational matrices of Haar wavelet method and compared the results of this method with the exact solution, they transformed the non-linear Murray equation into a linear algebraic equations that can be solved by Gauss-Jordan method
I. [5] studied an efficient numerical method for solution of non-linear generalized Burgers-Huxley equation based on the Haar wavelets approach, approximate solutions are compared with exact solutions
Summary
Boussinesq developed the original formulation of the governing equations for a free surface flow, which included the effects of surface waves, but in which the vertical. Ataie.andNajafi [3] are studied a higher-order two-dimensional Boussinesq wave model and they used the finite difference method in higher-order scheme for time and space in derived equations. Is using the FreeFem++ code to solve a three-parameter family of Boussinesq type systems in two space dimensions which approximate the three-dimensional Euler equations over an horizontal bottom. Many authors have studied the solution for partial differential equations by using the Haar wavelets method. AL-Rawi and Qasem [2] found the numerical solution for non-linear Murray equation by the operational matrices of Haar wavelet method and compared the results of this method with the exact solution, they transformed the non-linear Murray equation into a linear algebraic equations that can be solved by Gauss-Jordan method. [5] studied an efficient numerical method for solution of non-linear generalized Burgers-Huxley equation based on the Haar wavelets approach, approximate solutions are compared with exact solutions.
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