1. Boubaker Wavelets Functions: Properties and Applications
- Author
-
Eman H. Ouda, Samaa F. Ibraheem, and Suha Shihab
- Subjects
General Computer Science ,020209 energy ,General Mathematics ,Science ,General Physics and Astronomy ,02 engineering and technology ,General Chemistry ,01 natural sciences ,Agricultural and Biological Sciences (miscellaneous) ,General Biochemistry, Genetics and Molecular Biology ,Error analysis ,0103 physical sciences ,Botany ,0202 electrical engineering, electronic engineering, information engineering ,Boubaker polynomial, Collocation method, Convergence criteria, Error analysis, Wavelet polynomial ,010303 astronomy & astrophysics ,Mathematics - Abstract
This paper is concerned with introducing an explicit expression for orthogonal Boubaker polynomial functions with some important properties. Taking advantage of the interesting properties of Boubaker polynomials, the definition of Boubaker wavelets on interval [0,1) is achieved. These basic functions are orthonormal and have compact support. Wavelets have many advantages and applications in the theoretical and applied fields, and they are applied with the orthogonal polynomials to propose a new method for treating several problems in sciences, and engineering that is wavelet method, which is computationally more attractive in the various fields. A novel property of Boubaker wavelet function derivative in terms of Boubaker wavelet themselves is also obtained. This Boubaker wavelet is utilized along with a collocation method to obtain an approximate numerical solution of singular linear type of Lane-Emden equations. Lane-Emden equations describe several important phenomena in mathematical science and astrophysics such as thermal explosions and stellar structure. It is one of the cases of singular initial value problem in the form of second order nonlinear ordinary differential equation. The suggested method converts Lane-Emden equation into a system of linear differential equations, which can be performed easily on computer. Consequently, the numerical solution concurs with the exact solution even with a small number of Boubaker wavelets used in estimation. An estimation of error bound for the present method is also proved in this work. Three examples of Lane-Emden type equations are included to demonstrate the applicability of the proposed method. The exact known solutions against the obtained approximate results are illustrated in figures for comparison
- Published
- 2021