The first kind Chebyshev–Newton–Cotes quadrature rules (closed type) and its numerical improvement

2005 ◽  
Vol 168 (1) ◽  
pp. 479-495 ◽  
Author(s):  
M.R. Eslahchi ◽  
Mehdi Dehghan ◽  
M. Masjed-Jamei
Keyword(s):  
Quadrature Rules ◽  
Closed Type

A representation of the Peano kernel for some quadrature rules and applications

2006 ◽  
Vol 462 (2073) ◽  
pp. 2817-2832 ◽  
Author(s):  
Josip Pečarić ◽  
Nenad Ujević
Keyword(s):  
Quadrature Rules ◽  
Closed Type ◽  
Interpolating Polynomials ◽  
Effective Representation ◽  
Peano Kernel

A general interpolating formula is established. From this formula all Newton–Cotes quadrature rules of the closed type can be derived. Some corrected interpolating polynomials are also derived and used for obtaining corresponding quadrature rules. A new effective representation of the Peano kernel is derived. Estimation of errors for these quadrature rules is established.

scholarly journals Closed type families with overlapping equations

2014 ◽  
Vol 49 (1) ◽  
pp. 671-683 ◽  
Author(s):  
Richard A. Eisenberg ◽  
Dimitrios Vytiniotis ◽  
Simon Peyton Jones ◽  
Stephanie Weirich
Keyword(s):  
Closed Type

scholarly journals On Appel-Type Quadrature Rules

2002 ◽  
Vol 9 (3) ◽  
pp. 405-412
Author(s):  
C. Belingeri ◽  
B. Germano
Keyword(s):  
Remainder Term ◽  
Quadrature Rule ◽  
Bernoulli Numbers ◽  
Quadrature Rules ◽  
Rule Based ◽  
Numerical Example ◽  
The Given ◽  
Derivatives Of

Abstract The Radon technique is applied in order to recover a quadrature rule based on Appel polynomials and the so called Appel numbers. The relevant formula generalizes both the Euler-MacLaurin quadrature rule and a similar rule using Euler (instead of Bernoulli) numbers and even (instead of odd) derivatives of the given function at the endpoints of the considered interval. In the general case, the remainder term is expressed in terms of Appel numbers, and all derivatives appear. A numerical example is also included.

The equal coefficients quadrature rules and their numerical improvement

2005 ◽  
Vol 171 (2) ◽  
pp. 1331-1351 ◽  
Author(s):  
M.R. Eslahchi ◽  
Mehdi Dehghan ◽  
M. Masjed-Jamei
Keyword(s):  
Quadrature Rules
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