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

Shyam Lal, Deepak Kumar Singh

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

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DOI: http://dx.doi.org/10.23755/rm.v47i0.794

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