Numerical step-by-step integration proved to be a more effective method of analysis for multi-degree-of-freedom structural systems with significant non-linearity under a transient process of ground motion excitation.

Alan Turing searched for them on the Manchester Mark 1 in 1949, but the first successful identification of a Mersenne prime, M < sub > 521 </ sub >, by this means was achieved at 10: 00 P. M. on January 30, 1952 using the U. S. National Bureau of Standards Western Automatic Computer ( SWAC ) at the Institute for Numerical Analysis at the University of California, Los Angeles, under the direction of Lehmer, with a computer search program written and run by Prof. R. M.

Numerical approximations of roots of polynomial equations in one unknown is easily done on a computer by the Jenkins-Traub method, Laguerre's method, Durand – Kerner method or by some other root-finding algorithm.

Numerical quantities, even those denoted by letters, are usually printed in roman ( upright ) type, though sometimes can be italic.

*" Microscope Objectives: Numerical Aperture and Resolution " by Mortimer Abramowitz and Michael W. Davidson, Molecular Expressions: Optical Microscopy Primer ( website ), Florida State University, April 22, 2004.

*" Basic Concepts and Formulas in Microscopy: Numerical Aperture " by Michael W. Davidson, Nikon MicroscopyU ( website ).

Numerical weather prediction for forecasting involves complicated numeric computer models to predict weather accurately by taking many parameters in to account.

Its application to geomechanics problems is described in the book Numerical Modeling in Rock Mechanics, by Pande, G., Beer, G. and Williams, J. R ..

Many numerical computations are performed by the NAG Numerical Libraries, ATLAS libraries, or GMP libraries.

* Numerical analysis is a branch of mathematics, pioneered by celestial mechanicians, for calculating approximate numerical answers ( such as the position of a planet in the sky ) which are too difficult to solve down to a general, exact formula.

* Recognizing Numerical Constants by David H. Bailey and Simon Plouffe

* Black & White Records Numerical Listings, Online Discographical Project, research by Pete A. Grendysa, edited by Tyrone L. Settlemier ( born 1970 ), Albany, Oregon ( updated thru 18 August 2011 ), Steven Abrams ( publisher & managing editor )

* Numerical simulation ( 2. 6 MB ) ( or see 6. 2 MB version ), produced by Professor Nobuo Shuto of the Disaster Control Research Center, Tohoku University, Japan, shows the 1923 Kanto tsunami.

* The finite volume method by R. Eymard, T Gallouët and R. Herbin, update of the article published in Handbook of Numerical Analysis, 2000

This approach has been adopted by Boost C ++ Libraries, GNU Scientific Library and Numerical Recipes.

Numerical modeling techniques by Collins, et al.

Numerical designations stayed the same, however, and by late 1941 the division had completed its transition.

Richardson's interest in meteorology led him to propose a scheme for weather forecasting by solution of differential equations, the method used today, though when he published Weather Prediction by Numerical Process in 1922, suitable fast computing was unavailable.

He famously summarised the field in rhyming verse in Weather Prediction by Numerical Process ( p 66 ):

Numerical methods have been around much longer than computers have ( In the 1920s Richardson developed some of the finite difference schemes still in use today, but they were calculated by hand, using paper and pencil, by human " calculators "), but they have become very important through the availability of fast and cheap personal computers.

Numerical simulations suggest that stars ripped out from the dwarf would be spread out in a long stellar stream along its path, which were subsequently detected.

Numerical models of particle dynamics involving lateral differences in friction along the base of Olympus Mons have been shown to reproduce the volcano's present shape and asymmetry fairly well.

The wire frame format is also well suited and widely used in programming tool paths for DNC ( Direct Numerical Control ) machine tools.

Numerical modeling also provides new insights as observations and new discoveries are integrated into our physical understanding and then tested in computer simulations which validate new notions as well as produce entirely new theoretical findings, many of which are otherwise unattainable.

Numerical integration over more than one dimension is sometimes described as cubature, although the meaning of quadrature is understood for higher dimensional integration as well.

The argument order shown above is that of Gradshteyn and Ryzhik as well as Numerical Recipes.

The choice of sign is that of Abramowitz and Stegun as well as Gradshteyn and Ryzhik, but corresponds to the of Numerical Recipes.

Numerical weather models have limited forecast skill at spatial resolutions under, forcing complex wildfire models to parameterize the fire in order to calculate how the winds will be modified locally by the wildfire, and to use those modified winds to determine the rate at which the fire will spread locally .< ref name =" Clark-1996-CAF "> Although models such as Los Alamos ' FIRETEC solve for the concentrations of fuel and oxygen, the computational grid cannot be fine enough to resolve the combustion reaction, so approximations must be made for the temperature distribution within each grid cell, as well as for the combustion reaction rates themselves.

Category: Numerical integration ( quadrature )

* Numerical integration is often called ' numerical quadrature ' or simply ' quadrature '

* Numerical analysis – Approximate numerical solution of mathematical problems such as root-finding, integration, the solution of ordinary differential equations ; the approximation of special functions.

Numerical integration consists of finding numerical approximations for the value

Numerical integration methods can generally be described as combining evaluations of the integrand to get an approximation to the integral.

Numerical integration is one of the most intensively studied problems in numerical analysis.

* Numerical integration algorithms are found in GAMS class H2.

Category: Numerical integration ( quadrature )

* Numerical integration

Bateman is also author of Hydrodynamics and Numerical integration of differential equations.

* with Albert A. Bennett, William E. Milne: Numerical integration of differential equations, Bulletin of the National Research Council, 1933, Dover 1956

The Numerical Recipes books cover a range of topics that include both classical numerical analysis ( interpolation, integration, linear algebra, differential equations, and so on ), signal processing ( Fourier methods, filtering ), statistical treatment of data, and a few topics in machine learning ( hidden Markov models, support vector machines ).

* Numerical integration for calculating definite integrals

Numerical integration indicates that the coplanar, four-planet system is stable for at least another billion years.

* Numerical integration using the Romberg algorithm

The name is in analogy with quadrature meaning Numerical integration where weighted sums are used in methods such Simpson's method or the Trapezium rule.

* Numerical integration

* Numerical integration