A comparative study of numerical integration based on mixed quadrature rule and Haar wavelets

Abstract

This note deals with the problem of determining the approximate solution of real definite integrals. Approximating the solution of given  real definite integrals here is done by means of mixed quadrature rule which is then  compared with the Haar wavelets for single, double and improper integrals. The main advantage of the proposed numerical integration method over Haar wavelets is its efficiency, lesser functional evaluation and simple applicability. Some numerical examples are provided to illustrate the accuracy and relative error of the proposed rule.