Approximation of a function by the extended Chebyshev wavelet method of first kind and its applications

Abstract

In this paper, we have first introduced the Extended Chebyshev wavelet of first kind. Then, it is used to calculate the approximation error of a function having its first and second derivatives bounded. Also, we have solved various differential equations like the Hermite differential equation of order zero, nonlinear Riccati differential equation, and differential equation corresponding to radioactive decay using this wavelet technique to show the usefulness of this method.