Approximations of a function whose first and second derivatives belonging to generalized Hölder’s class by extended Legendre wavelet method and its applications in solutions of differential equations

Abstract

In this paper, the generalized Holder’s class and extended Legendre wavelet are studied. The wavelet approximations of a function whose first and second derivatives belonging to generalized Holder’s class by extended Legendre wavelets have been determined. Two corollaries have been obtained by the main theorems of this paper. Linear and non-linear differential equations have been solved by extended Legendre wavelet methods.