A comparative study of Gauss{Laguerre quadrature and an open type mixedquadrature by evaluating some improper integrals

Abstract

An open type mixed quadrature rule is constructed blending the anti-Gauss 3-point rule with Steffensen's4-point rule. The analytical convergence of the mixed rule is studied. An adaptive integration scheme is designed basedon the mixed quadrature rule. A comparative study of the mixed quadrature rule and the Gauss{Laguerre quadraturerule is given by evaluating several improper integrals of the form1∫0exf(x)dx. The advantage of implementing mixedquadrature rule in developing an efficient adaptive integration scheme is shown by evaluating some improper integrals.