A Mixed Quadrature Rule by Blending Clenshaw-Curtis and Gauss-Legendre Quadrature Rules for Approximate Evaluation of Real Definite Integrals

Anasuya Pati,Pritikanta Patra,Rajani B Dash

doi:10.18052/www.scipress.com/bsmass.2.10

Anasuya Pati, Pritikanta Patra + Show 1 more

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https://doi.org/10.18052/www.scipress.com/bsmass.2.10

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Abstract

A mixed quadrature rule blending Clenshaw-Curtis five point rule and Gauss-Legendre three point rule is formed. The mixed rule has been tested and found to be more effective than that of its constituent Clenshaw-Curtis five point rule.

Highlights

Real definite integrals of the type (1.1)have been successfully approximated by several authors by applying the mixed quadrature rule
An n-point Gauss rule is of precision 2n-1, while the precision of an n-point Clenshaw Curtis rule is n
In general Gauss type rule is of higher precision than that of Clenshaw-Curtis type rule when same abscissae are used

Summary

Introduction

I. INTRODUCTION Real definite integrals of the type have been successfully approximated by several authors by applying the mixed quadrature rule. An n-point Gauss rule is of precision 2n-1, while the precision of an n-point Clenshaw Curtis rule is n. In general Gauss type rule is of higher precision than that of Clenshaw-Curtis type rule when same abscissae are used. In this paper, taking the advantage of the fact that Gauss-Legendre 3-point rule and ClenshawCurtis 5-point rule are of same precision (i.e. precision 5), we formed a mixed quadrature rule of higher precision (i.e. precision 7) taking linear combination of these rules.

Results

Conclusion