scholarly journals Quadrature Formula Study for the Integral with Hilbert Kernel based on Trigonometric Interpolational Polynomial

2017 ◽  
Vol 10 (01) ◽  
pp. 1-6
Author(s):  
Almaz Ferdinantovich Gilemzyanov
Keyword(s):  
Quadrature Formula ◽  
Hilbert Kernel

scholarly journals Quadrature Formula Study for the Integral with Hilbert Kernel based on Trigonometric Interpolational Polynomial

2017 ◽  
Vol 10 (1) ◽  
Author(s):  
Almaz Ferdinantovich Gilemzyanov ◽  
Anis Fuatovich Galimyanov ◽  
Chulpan Bakievna Minnegalieva
Keyword(s):  
Quadrature Formula ◽  
Hilbert Kernel

scholarly journals Simpson type inequalities and applications

2021 ◽  
Author(s):  
Muhammad Uzair Awan ◽  
Muhammad Zakria Javed ◽  
Michael Th. Rassias ◽  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor
Keyword(s):  
Quadrature Formula ◽  
Convex Functions ◽  
Integral Identity ◽  
Higher Order ◽  
Auxiliary Result ◽  
First Order ◽  
New Class ◽  
Differentiable Functions

AbstractA new generalized integral identity involving first order differentiable functions is obtained. Using this identity as an auxiliary result, we then obtain some new refinements of Simpson type inequalities using a new class called as strongly (s, m)-convex functions of higher order of $$\sigma >0$$ σ > 0 . We also discuss some interesting applications of the obtained results in the theory of means. In last we present applications of the obtained results in obtaining Simpson-like quadrature formula.

scholarly journals Optimal quadrature formula in the sense of Sard in K2(P3) space

2014 ◽  
Vol 95 (109) ◽  
pp. 29-47 ◽  
Author(s):  
Abdullo Hayotov ◽  
Gradimir Milovanovic ◽  
Kholmat Shadimetov
Keyword(s):  
Hilbert Space ◽  
Sobolev Space ◽  
Quadrature Formula ◽  
Asymptotic Optimality ◽  
Trigonometric Functions ◽  
Numerical Examples ◽  
Optimal Quadrature Formula ◽  
Optimal Quadrature ◽  
Optimal Coefficients ◽  
Optimal Formula

We construct an optimal quadrature formula in the sense of Sard in the Hilbert space K2(P3). Using Sobolev?s method we obtain new optimal quadrature formula of such type and give explicit expressions for the corresponding optimal coefficients. Furthermore, we investigate order of the convergence of the optimal formula and prove an asymptotic optimality of such a formula in the Sobolev space L (3)2 (0, 1). The obtained optimal quadrature formula is exact for the trigonometric functions sin x, cos x and for constants. Also, we include a few numerical examples in order to illustrate the application of the obtained optimal quadrature formula.

scholarly journals On Solving Hyperbolic Trajectory Using New Predictor-Corrector Quadrature Algorithms

2014 ◽  
Vol 11 (1) ◽  
pp. 186-192
Author(s):  
Baghdad Science Journal
Keyword(s):  
Quadrature Formula ◽  
Grid Size ◽  
Hyperbolic Orbit ◽  
Efficient Manner ◽  
Hyperbolic Case ◽  
Eccentric Anomaly ◽  
Kepler’S Equation ◽  
Orbit Equation ◽  
Predictor Corrector ◽  
Better Than

In this Paper, we proposed two new predictor corrector methods for solving Kepler's equation in hyperbolic case using quadrature formula which plays an important and significant rule in the evaluation of the integrals. The two procedures are developed that, in two or three iterations, solve the hyperbolic orbit equation in a very efficient manner, and to an accuracy that proves to be always better than 10-15. The solution is examined with and with grid size , using the first guesses hyperbolic eccentric anomaly is and , where is the eccentricity and is the hyperbolic mean anomaly.

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.

An optimal quadrature formula in the Sobolev space

2021 ◽  
Vol 65 (3) ◽  
pp. 46-59
Keyword(s):  
Sobolev Space ◽  
Quadrature Formula ◽  
Approximate Calculation ◽  
Order Of Convergence ◽  
Quadrature Formulas ◽  
Explicit Formulas ◽  
Optimal Quadrature Formula ◽  
Optimal Quadrature ◽  
Optimal Coefficients ◽  
Optimal Quadrature Formulas

This paper studies the problem of construction of optimal quadrature formulas for approximate calculation of integrals with trigonometric weight in the L(2m)(0, 1) space for any ω ൐= 0, ω ∈ R. Here explicit formulas for the optimal coefficients are obtained. We study the order of convergence of the optimal formulas for the case m = 1, 2. The obtained optimal quadrature formulas are exact for Pm−1(x), where Pm−1(x) is a polynomial of degree (m − 1).

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