# numerical integration

## numerical integration

[nü′mer·i·kəl ‚int·ə′grā·shən]
(mathematics)
The process of using a set of approximate values of a function to calculate its integral to comparable accuracy.
References in periodicals archive ?
We remark that "truncated" processes with respect to Laguerre weights were introduced in numerical quadrature by Mastroianni and Monegato [13,14] and successively applied to different kinds of integrals (for instance [2, 16]), whereas "truncated" Lagrange polynomial sequences on the semi-axis were introduced in [10, 12] (see also [20, 24]) and on the real line in [15] (see, also, [22, 23]).
This is a major contribution introduced here, where random numerical quadrature formulae are applied to approximate the solution s.p.
It is found that those semi-infinite integrals with respect to [xi] can be accurately evaluated by employing the numerical quadrature scheme based on 21-point Gauss-Kronrod rule [33].
As a result, with the help of mapped numerical quadrature, we obtain highly accurate computed stresses.
In these cases the multiple integrals are approximated as accurately as required using numerical quadrature, generally rectangular quadrature over q equally spaced points (Bock & Mislevy, 1982).
For most of the book he writes code in the Fortran programming language using the GNU Emacs text editor and command line compiling from the Cygwin "shell" for Windows, which uses the GNU Fortran compiler "gfortran." He covers getting comfortable, interpolation and data fitting, searching for roots, numerical quadrature, ordinary differential equations, Fourier analysis, Monte Carlo method, partial differential equations, advanced numerical quadrature, advanced ordinary differential equation solver and applications, and high performance computing.
Wang, "An inequality of Ostrowski-Gruss' type and its applications to the estimation of error bounds for some special means and for some numerical quadrature rules," Computers & Mathematics with Applications, vol.
Wang, An inequality of Ostrowski- Gruss type and its applications to the estimation of error bounds for some special means and for some numerical quadrature rules, Comput.Math.
Only functional evaluations are required in these closed-form expressions without quadrature errors, and the evaluation perform more efficient than numerical quadrature techniques [8], such as Gauss-Legendre Quadrature (GLQ).
Burg, "Derivative-based closed Newton-Cotes numerical quadrature," Applied Mathematics and Computation, vol.
Stroud, "Initial value problems for ordinary differential equations," in Numerical Quadrature and Solution of Ordinary Differential Equations, pp.
Numerical quadrature of analytic and harmonic functions.

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