Error estimation for quadrature formulas based on equally spaced nodes

Abstract

The error estimation for quadrature formulas based on equally spaced nodes is discussed in this paper. The error estimates use embedded formulas and they are obtained for Newton‐Cotes and Hermitian quadrature formulas. The coefficients of these formulas and error estimates are presented. The locally adaptive integration procedures implementing the truncation error estimation method proposed in this paper were developed in MATLAB and results of appropriate comparative tests are presented.

Key words:

• numerical integration
• quadrature formula
• error estimate
• locally adaptive procedure