Results 11 to 20 of about 1,730 (224)

The Optimal Quadrature Formula of Approximate Calculation of Curvilinear Integral of First Kind for Some Classes of Functions and Curves

Моделирование и анализ информационных систем, 2013
In this paper is considered the extreme problem of searching for the optimal quadrature formulas in S.M. Nikolskiy sense for approximate calculation of curvilinear integrals of first kind on the class of differentiable functions, the second gradient norm
K. Tukhliev
doaj   +4 more sources

The numerical solution of an Abel integral equation by the optimal quadrature formula

Results in Applied Mathematics
In this study, a novel and efficient approach utilizing optimal quadrature formulas is introduced to derive approximate solutions for generalizing Abel’s integral equations. The method, characterized by high accuracy and simplicity, involves constructing
Abdullo Hayotov, Samandar Babaev, Bobomurod Boytillayev   +2 more
doaj   +2 more sources

Uniqueness of the Optimal Nodes of Quadrature Formulae [PDF]

Mathematics of Computation, 1981
We prove the uniqueness of the quadrature formula with minimal error in the space W
Borislav D. Bojanov
openaire   +3 more sources

On an Optimal Quadrature Formula for Classes of Functions Given by Modulus of Continuity

Моделирование и анализ информационных систем, 2014
The problem of minimizing the error of a cubature formula on the classes of functions given by modulus of continuity for cubature formulas with fixed nodes on the boundary of gird rectangular localization domain of nodes is considered.
M. Sh. Shabozov
doaj   +2 more sources

Weighted Optimal Formulas for Approximate Integration

Mathematics
Solutions to problems arising from much scientific and applied research conducted at the world level lead to integral and differential equations. They are approximately solved, mainly using quadrature, cubature, and difference formulas. Therefore, in the
Kholmat Shadimetov, Ikrom Jalolov
doaj   +2 more sources

Multilevel quadrature formulae for the optimal control of random PDEs [PDF]

Numerische Mathematik
Abstract This manuscript presents a framework for using multilevel quadrature formulae to compute the solution of optimal control problems constrained by random partial differential equations. Our approach consists in solving a sequence of optimal control problems discretized with different levels of accuracy of the physical and ...
Fabio Nobile, Tommaso Vanzan
core   +6 more sources

AN OPTIMAL QUADRATURE FORMULA OF CLOSED TYPE [PDF]

AN OPTIMAL QUADRATURE FORMULA OF CLOSED TYPE
application/pdf An optimal 3-point quadrature formula of closed type is derived. The optimality is considered with respect to a given way of estimation of its error.
Ujevic, Nenad, 29958
core   +2 more sources

Optimal Quadrature Formulas with Derivatives in the Space

, 2021
In the paper we consider an extension problem of the Euler-Maclaurin quadrature formula in the space   by constructing an optimal quadrature ...
Rashidjon, Rasulov, Sattorov, Abdusalom
core   +1 more source

Estimates of the error of interval quadrature formulas on some classes of differentiable functions

Researches in Mathematics, 2020
The exact value of error of interval quadrature formulas $$\int_0^{2\pi}f(t)dt -\frac{\pi}{nh}\sum_{k=0}^{n-1}\int_{-h}^hf(t+\frac {2k\pi}{n})dt = R_n(f;\vec{c_0};\vec{x_0};h)$$ obtained for the classes $W^rH^{\omega} (r=1,2,...)$ of differentiable ...
V.P. Motornyi, D.A. Ovsyannikov
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Polynomial Spline Collocation Method for Solving Weakly Regular Volterra Integral Equations of the First Kind

Известия Иркутского государственного университета: Серия "Математика", 2022
The polynomial spline collocation method is proposed for solution of Volterra integral equations of the first kind with special piecewise continuous kernels.
Aleksandr Tynda, Samad Noeiaghdam, Denis Sidorov   +2 more
doaj   +1 more source