Bulletin of Pure & Applied Sciences- Mathematics and Statistics
  • Year: 2020
  • Volume: 39e
  • Issue: 2

A mixed quadrature rule of modified Birkhoff-Young rule and SM2(f) rule for the numerical integration of analytic functions*

1. Department of Mathematics, B.S. College, Nuahat, Jajpur, Odisha754024, India.

†Corresponding author Sanjit Kumar Mohanty, E-mail: dr.sanjitmohanty@rediffmail.com

Abstract

A quadrature rule of higher precision is constructed in this paper by mixing two quadrature rules of lower precision for an approximate evaluation of the integral of an analytic function over a line segment in the complex plane. An asymptotic error estimate of the rule is also determined and the rule is numerically verified.

Keywords

Quadrature rule, Asymptotic error, Analytic function, Numerical integration, Modified Birkhoff-Young rule, Richardson Extrapolation, SM2 (f), SM6 (f), ESM2, ESM6