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.
Highlights
As a powerful mathematical tool, Wavelet analysis has been widely used in image digital processing, quantum field theory, numerical analysis and many other fields in the recent years.Haar wavelets have been applied extensively for signal processing in communications and physics research, and more mathematically focused on differential equations and even non-linear problems
After discrediting the differential equation in a conventional way like the finite difference approximation, wavelets which can be used for algebraic manipulations in the system of equations obtained which may lead to better condition number of the resulting system [10]
We study the numerical solution for non-linear third-order boussinesq system by the operational matrices of Haar wavelet method and we compare the results of this method with the exact solution
Summary
As a powerful mathematical tool, Wavelet analysis has been widely used in image digital processing, quantum field theory, numerical analysis and many other fields in the recent years. Anotonopoulos et al [2] are studing three initial-boundary-value problems for Bona-Smith family of Boussinesq systems corresponding, respectively, to nonhomogeneous Dirichlet, reflection, and periodic boundary conditions posed at the endpoints of a finite spatial interval, and establish existence and uniqueness of their solutions. Numerical Solution for Non-linear Boussinesq System Using the Haar Wavelet Method simple feedback controls are constructed such that the resulting closed-loop systems are exponentially stable. We study the numerical solution for non-linear third-order boussinesq system by the operational matrices of Haar wavelet method and we compare the results of this method with the exact solution.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
