A New Formula of Numerical Integration Based on Legendre Wavelets

Abstract

This work aims to establish a new numerical formula to estimate the simple integral\begin{equation*}I = \int_a^b f (t)dt,\end{equation*}where f a given function integrable over a bounded interval [a,b].This formula is based on the decomposition of the function f in the Hilbertian basis of L2(]0,l[), formed by Legendre wavelets.Illustrative examples have been discussed to demonstrate the validity and applicability of the formula, the results obtained have been compared with those given by the three generalized Newton-cotes formulas; the formula of the midpoint, of the trapeze and of Simpson.