Results 1 to 10 of about 575 (217)
Exactness of Quadrature Formulas [PDF]
SIAM Review, 2022 The standard design principle for quadrature formulas is that they should be exact for integrands of a given class, such as polynomials of a fixed degree. We show how this principle fails to predict the actual behavior in four cases: Newton-Cotes, Clenshaw-Curtis, Gauss-Legendre, and Gauss-Hermite quadrature.
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Hermite–Hadamard–Fejér-Type Inequalities and Weighted Three-Point Quadrature Formulae
Mathematics, 2021 The goal of this paper is to derive Hermite–Hadamard–Fejér-type inequalities for higher-order convex functions and a general three-point integral formula involving harmonic sequences of polynomials and w-harmonic sequences of functions. In special cases,
Mihaela Ribičić Penava
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Orthogonal polynomials and generalized Gauss-Rys quadrature formulae
Kuwait Journal of Science, 2021 Orthogonal polynomials and the corresponding quadrature formulas of Gaussian type with respect to the even weight function $\omega^{\lambda}(t;x)=\exp(-x t^2)(1-t^2)^{\lambda-1/2}$ on $(-1,1)$, with parameters $\lambda>-1/2$ and $x>0$, are considered.
Gradimir Milovanovic, Nevena Vasovic ́
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Some Generalized Error Inequalities and Applications
Journal of Inequalities and Applications, 2008 We present a family of four-point quadrature rule, a generalization of Gauss-two point, Simpson's 3/8, and Lobatto four-point quadrature rule for twice-differentiable mapping.
Nazir Ahmad Mir, Fiza Zafar
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On semicardinal quadrature formulae [PDF]
Mathematics of Computation, 1974 The present paper concerns the semicardinal quadrature formulae introduced in Part III of the reference [3]. These were the limiting forms of Sard’s best quadrature formulae as the number of nodes increases indefinitely. Here we give a new derivation and characterization of these formulae.
Schoenberg, I. J., Silliman, S. D.
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Numerical study of nonlinear problems in the dynamics of thin-walled structural elements [PDF]
E3S Web of Conferences, 2021 Mathematical model of the problem of vibration of thin-walled structural elements has been constructed based on Kirchhoff-Love theory. The problem is reduced, using the Bubnov-Galerkin method, to the solution of a set of nonlinear integro-differential ...
Kucharov Olim +3 more
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Stochastic Quadrature Formulas [PDF]
Mathematics of Computation, 1969 A class of formulas for the numerical evaluation of multiple integrals is described, which combines features of the Monte-Carlo and the classical methods. For certain classes of functions—defined by smoothness conditions—these formulas provide the fastest possible rate of convergence to the integral. Asymptotic error estimates are derived, and a method
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On Birkhoff Quadrature Formulas [PDF]
Proceedings of the American Mathematical Society, 1986 In an earlier work the author has obtained new quadrature formulas (see (1.3)) based on function values and second derivatives on the zeros of
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Construction of Compact Finite Difference Schemes by Classic Differential Quadrature
Applied Sciences, 2017 Using classic differential quadrature formulae and uniform grids, this paper systematically constructs a variety of high-order finite difference schemes, and some of these schemes are consistent with the so-called boundary value methods.
Fangzong Wang, Mingshuai Pan, Yong Wang
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Quadrature Formulae with Non-Negative Coefficients for Poisson and Dinie Integrals
Наука и техника, 2005 Special quadrature formulae with non-negative coefficients for the Poisson and Dinie integrals have been derived. Even estimations of approximate formula errors permit to conduct calculations with the given accuracy.
I. N. Meleshko
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