Approximation and moduli of continuity for a function belonging to Holder’s class Hα [0, 1) and solving Lane-Emden differential equation by Boubaker wavelet technique

Abstract

In this paper, Boubaker wavelet is considered. The Boubaker wavelets are orthonormal. The series of this wavelet is verified for the function f(t) = t. The convergence analysis of solution function of Lane-Emden differential equation has been studied. New Boubaker wavelet estimator E2 k,M(f) for the approximation of solution function f belong to H¨older’s class Hα[0, 1) of order 0 < α ≤ 1, has been devloped. Furthermore, the moduli of continuity of solution function of Lane-Emden differential equation has been introduced and it has been estimated for solution function f∈ Hα[0, 1) class. These estimator and moduli of continuity are new and best possible in wavelet analysis. Boubaker wavelet collocation method has been proposed to solve Lane-Emden differential equations with unkown Boubaker coefficients. In this process, Lane-Emden differential equations are reduced into a system of algebraic equations and these equations are solved by collocation method. Three Lane-Emden type equations are solved to demonstrate the applicability of the proposed method. The solutions obtained by the proposed method are compared with their exact solutions. The absolute errors are negligible. Thus,this shows that the method described in this paper is applicable and accurate.

Keywords

• boubaker wavelet, boubaker polynomial, boubaker wavelet approximation, moduli of continuity, collocation method, lane-emden differential equations