نتایج جستجو برای: newton cotes formula

تعداد نتایج: 111465  

1996
Jürgen Ehlers

A frame theory encompassing general relativity and Newton–Cartan theory is reviewed. With its help, a definition is given for a one-parameter family of general relativistic spacetimes to have a Newton–Cartan or a Newtonian limit. Several examples of such limits are presented. PACS numbers: 0420, 0240, 0450

Journal: :Journal of Computational and Applied Mathematics 1994

1998
SVEN EHRICH

Gauss-Kronrod product quadrature formulas for the numerical approximation of R 1 ?1 k(x)f (x)dx are shown to converge for every Riemann integrable f , and to possess optimal stability. Similar results are proved for the product formulas based on the Kronrod nodes only. An application to the uniform convergence of approximate solutions of integral equations is given.

2013
Mohsin Javed Lloyd N. Trefethen

The error in the trapezoidal rule quadrature formula can be attributed to discretization in the interior and non-periodicity at the boundary. Using a contour integral, we derive a unified bound for the combined error from both sources for analytic integrands. The bound gives the Euler–Maclaurin formula in one limit and the geometric convergence of the trapezoidal rule for periodic analytic func...

2008
Fiza Zafar Nazir Ahmad Mir

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. Moreover, it is shown that the corresponding optimal quadrature formula presents better estimate in the context of four-point quadrature formulae of closed type. A unified treatment of error inequalities for different cla...

2005
BORISLAV BOJANOV Laura Gori

We discuss quadrature formulae of highest algebraic degree of precision for integration of functions of one or many variables which are based on non-standard data, i.e., in which the information used is different from the standard sampling of function values. Among the examples given in this survey is a quadrature formula for integration over the disk, based on linear integrals on n chords, whi...

2013
Christian Göge

This thesis discusses strategies for numerically solving a two dimensional integral. The difficulties here are due to numerous integrands and regions in R2. The transformation to units as the 2-simplex and the cube can simplify many integrands. An approach to arbitrary regions is to decompose them into easy ones as triangles and rectangles. For these regions formulas that approximate the two di...

Journal: :Journal of mathematical analysis and modeling 2022

In this paper, using a new identity, we study one of the famous Newton-Cotes three-point quadraturerules. More precisely Maclaurin’s quadrature rule, for which establish error estimate methodunder constraint that first derivatives belong to class preinvex functions. We also give someapplications special means as applications. believe studied inequality and resultsobtained in article will furthe...

Journal: :Math. Comput. 1996
Laura Gori Charles A. Micchelli

The main purpose of this paper is the construction of explicit Gauss-Turán quadrature formulas: they are relative to some classes of weight functions, which have the peculiarity that the corresponding s-orthogonal polynomials, of the same degree, are independent of s. These weights too are introduced and discussed here. Moreover, highest-precision quadratures for evaluating Fourier-Chebyshev co...

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