scholarly journals Ostrowski type inequalities and some selected quadrature formulae

2020 ◽  
pp. 54-54
Author(s):  
Gradimir Milovanovic
Keyword(s):  
Numerical Integration ◽  
Error Term ◽  
Quadrature Formulas ◽  
Quadrature Formulae ◽  
Survey Paper ◽  
Ostrowski’S Inequality ◽  
Basic Facts ◽  
Peano Kernel

Some selected Ostrowski type inequalities and a connection with numerical integration are studied in this survey paper, which is dedicated to the memory of Professor D. S. Mitrinovic, who left us 25 years ago. His significant inuence to the development of the theory of inequalities is briefly given in the first section of this paper. Beside some basic facts on quadrature formulas and an approach for estimating the error term using Ostrowski type inequalities and Peano kernel techniques, we give several examples of selected quadrature formulas and the corresponding inequalities, including the basic Ostrowski's inequality (1938), inequality of Milovanovic and Pecaric (1976) and its modifications, inequality of Dragomir, Cerone and Roumeliotis (2000), symmetric inequality of Guessab and Schmeisser (2002) and asymmetric in-equality of Franjic (2009), as well as four point symmetric inequalites by Alomari (2012) and a variant with double internal nodes given by Liu and Park (2017).

scholarly journals Closed expressions for coefficients in weighted Newton-Cotes quadratures

Filomat ◽  
2013 ◽  
Vol 27 (4) ◽  
pp. 649-658 ◽  
Author(s):  
Mohammad Masjed-Jamei ◽  
Gradimir Milovanovic ◽  
M.A. Jafari
Keyword(s):  
Short Note ◽  
Stirling Numbers ◽  
Quadrature Formulas ◽  
Numerical Examples ◽  
Quadrature Formulae ◽  
Equidistant Nodes

In this short note, we derive closed expressions for Cotes numbers in the weighted Newton-Cotes quadrature formulae with equidistant nodes in terms of moments and Stirling numbers of the first kind. Three types of equidistant nodes are considered. The corresponding program codes in Mathematica Package are presented. Finally, in order to illustrate the application of the obtained quadrature formulas a few numerical examples are included.

On the error term of the filon quadrature formulae

1987 ◽  
Vol 27 (1) ◽  
pp. 85-97 ◽  
Author(s):  
Ulf Torsten Ehrenmark
Keyword(s):  
Error Term ◽  
Quadrature Formulae

A Proof of the Newton-Cotes Quadrature Formulas with Error Term

1970 ◽  
Vol 77 (10) ◽  
pp. 1065-1072 ◽  
Author(s):  
D. R. Hayes ◽  
L. Rubin
Keyword(s):  
Error Term ◽  
Quadrature Formulas

scholarly journals Orthogonal polynomials and generalized Gauss-Rys quadrature formulae

2021 ◽  
Vol 49 (1) ◽  
Author(s):  
Gradimir V. Milovanovic ◽  
◽  
Nevena Vasovic ◽  
Keyword(s):  
Orthogonal Polynomials ◽  
Quadrature Rules ◽  
Quadrature Formulas ◽  
Numerical Construction ◽  
Quadrature Formulae ◽  
Gaussian Type ◽  
Modified Moments

Orthogonal polynomials and the corresponding quadrature formulas of Gaussian type concerni λ ng > the 1 e / v 2 en wei x gh > t f 0 unction ω(t; x) = exp λ (−= xt 1 2) / ( 2 1 − t2)−1/2 on (−1, 1), with parameters − and , are considered. For these quadrature rules reduce to the socalled Gauss-Rys quadrature formulas, which were investigated earlier by several authors, e.g., Dupuis at al 1976 and 1983; Sagar 1992; Schwenke 2014; Shizgal 2015; King 2016; Milovanovic ´ 2018, etc. In this generalized case, the method of modified moments is used, as well as a transformation of quadratures on (−1, 1) with N nodes to ones on (0, 1) with only (N + 1)/2 nodes. Such an approach provides a stable and very efficient numerical construction.

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