On families of quadrature formulas based on Euler identities

• Published in: Applied mathematics and computation Vol. 217; no. 9; pp. 4516 - 4528
• Main Authors: FRANJIC, Iva, PECARIC, Josip, PERIC, Ivan
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 2011; Elsevier
• Subjects: Algebra; Bernoulli polynomials; Closed 5-point quadrature formulas; Computation; Corrected quadrature formulas; Derivatives; Exact sciences and technology; Extended Euler formulas; Gauss formulas; Intervals; Lobatto formulas; Mathematical analysis; Mathematical models; Mathematics; Number theory; Numerical analysis; Numerical analysis. Scientific computation; Quadratures; Real functions; Sciences and techniques of general use; Sharp estimates of error; Corrected quadrature formulas; Extended Euler formulas; Gauss formulas; Bernoulli polynomials; Closed 5-point quadrature formulas; Sharp estimates of error; Lobatto formulas; Polynomial; Numerical integration; Error estimation; Gauss formula; Numerical analysis; Applied mathematics; Quadrature formula
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2010.11.002

A family consisting of quadrature formulas which are exact for all polynomials of order ⩽5 is studied. Changing the coefficients, a second family of quadrature formulas, with the degree of exactness higher than that of the formulas from the first family, is produced. These formulas contain values of the first derivative at the end points of the interval and are sometimes called “corrected”.