Definite Quadrature Formulae of Order Three Based on the Compound Midpoint Rule

2019 ◽  
pp. 227-234
Author(s):  
Ana Avdzhieva ◽  
Vesselin Gushev ◽  
Geno Nikolov
Keyword(s):  
Midpoint Rule ◽  
Quadrature Formulae

scholarly journals Some Quadrature-Formulae

1900 ◽  
Vol s1-32 (1) ◽  
pp. 258-277 ◽  
Author(s):  
W. F. Sheppard
Keyword(s):  
Quadrature Formulae

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.

Gaussian Interval Quadrature Formulae for Tchebycheff Systems

2005 ◽  
Vol 43 (2) ◽  
pp. 787-795 ◽  
Author(s):  
Borislav Bojanov ◽  
Petar Petrov
Keyword(s):  
Quadrature Formulae

scholarly journals Calculation of Chakalov-Popoviciu quadratures of Radau and Lobatto type

2002 ◽  
Vol 43 (3) ◽  
pp. 429-447 ◽  
Author(s):  
Miodrag M. Spalević
Keyword(s):  
Numerical Method ◽  
Quadrature Formula ◽  
Spline Function ◽  
Finite Interval ◽  
Analytic Formula ◽  
Numerical Results ◽  
Quadrature Formulae

AbstractA numerical method for calculation of the generalized Chakalov-Popoviciu quadrature formulae of Radau and Lobatto type, using the results given for the generalized Chakalov-Popoviciu quadrature formula, is given. Numerical results are included. As an application we discuss the problem of approximating a function f on the finite interval I = [a, b] by a spline function of degree m and variable defects dv, with n (variable) knots, matching as many of the initial moments of f as possible. An analytic formula for the coefficients in the generalized Chakalov-Popoviciu quadrature formula is given.

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