Estimation of Approximation Error of a function having its derivatives belonging to Lipschitz class of order - by Extended Legendre Wavelet (ELW) method and its applications

Abstract

In this paper, the approximation errors of a function having its derivatives belonging to the Lipschitz class of order - alpha by the ELW method have been obtained. We have solved various differential equations like the Hermite differential equation, Riccati differential equation, Blasius equation, radioactive decay problem by using this method. Also, we have approximated the sum of some specic series that is not convergent by traditional methods.