Moduli of continuity of functions in Holder’s class by First kind Chebyshev Wavelets and Its Applications in the Solution of Lane-Emden Differential Equations

Abstract

In this paper , two new moduli of continuityand two estimators E2k−1,0 and,E2k−1,M of a functions f in H¨older’s class Hα,2ωk [0, 1) by First kind Chebyshev Wavelets have been determined. These moduli of continuity and estimators are new and best possible in wavelet analysis. Applying this technique ,Lane -Emden differential equations have been solved by first kind Chebyshev wavelet method.These solutions obtained by first kind Chebyshev wavelet method are approximately coincided with their exact solutions. This is a significant achievement of this research paper in wavelet analysis.

Keywords

• chebyshev wavelet, modulus of continuity, chebyshev wavelet approximation, function of h¨older’s class, orthonormal basis, operational matrix of integration for first kind chebyshev wavelet