The approximations of a function belonging Hölder class Hα[0,1) by second kind Chebyshev wavelet method and applications in solutions of differential equation

Abstract

In this paper, two new estimates [Formula: see text] and [Formula: see text] of a function [Formula: see text] belonging to [Formula: see text] are obtained by Chebyshev wavelet method. These estimators are new, sharper and best possible in Wavelet Analysis. Using this method, the solutions of four differential equations are obtained. These solutions are approximately the same as exact solutions.

Chebyshev Wavelet Analysis

“…We note that the first derivative in (27) depends on U m−1 ðxÞ, i.e., Chebyshev polynomials of the second kind. More specifically, it can be written as a Chebyshev wavelet of the second kind (see [20]). The computation of the derivatives ( 26) is more complicated for p > 1.…”

“…Current literature showed that these methods depends on the different operational matrices in the sense of [17][18][19]. Moreover, Chebyshev wavelets provided sharp estimates of functions in Hölder spaces of order α [20].…”