Some Fully Symmetric Quadrature Rules for Approximation of Complex Line Integral

Abstract

This paper is concerned with the construction of some quadrature rules of algebraic degree of precision nine, thirteen and seventeen for the approximate evaluation of integrals of an analytic function on a line segment in the complex plane. The nodes in each of the rules constructed are symmetrically situated about the contour of integration. Asymptotic error estimate of each rule has been derived and a comparative study regarding the accuracy in approximations obtained by the rules constructed has been studied. Some standard integrals of analytic functions have been numerically integrated by the quadrature rules constructed in this paper to substantiate the conclusion drawn on the relative efficiency of the rules.