Numerical methods calculate the positions and velocities of the objects a short time in the future, then repeat the calculation.

Numerical values associated with the calculation of availability are often awkward, consisting of a series of 9s before reaching any significant numerical information ( e. g. 0. 9999999654 ).

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

Numerical evaluation of is a bit trickier due to the matrix exponential integral.

* Smith III, F. L. and C. Smith, Numerical evaluation of Chapman's grazing incidence integral ch ( X, χ ), J. Geophys.

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.

* Kawaguchi, T., Tanaka, T. and Tsuji, Y., Numerical simulation of two-dimensional fluidized beds using the discrete element method ( comparison between the two-and three-dimensional models ) Powder Technology, 96 ( 2 ): 129 – 138, 1998.

In early 1954, a committee of the Joint Chiefs of Staff requested that the two machines be compared for the purpose of using them for a Joint Numerical Weather Prediction project.

In early 1954, a committee of the Joint Chiefs of Staff requested that the two machines be compared for the purpose of using them for a Joint Numerical Weather Prediction project.

* Numerical representation of time using a 24-hour clock, hh: mm: ss for hours, minutes, seconds

Numerical analysis specifically tries to estimate this error when using approximation equations and / or algorithms, especially when using finitely many digits to represent real numbers ( which in theory have infinitely many digits ).

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.

By the early 1990s, when Second Edition versions of Numerical Recipes ( with code in C, Fortran-77, and Fortran-90 ) were published, it was clear that the constituency for Numerical Recipes was by no means the majority of scientists doing computation, but only that slice that lived between the more mathematical numerical analysts and the larger community using integrated environments.

* “ Numerical Calculation of Edge Diffraction, using Reciprocity ” David Ingham, Proc.

Numerical modelling using computational fluid dynamics has also been used extensively in the study of cyclonic behaviour.

Production forecasting of CBM wells and fields can be performed using specialised Material Balance tools or Numerical simulators, as it requires an explicit coupling of the matrix gas diffusion process with the flow within fractures ( Darcy law applies ).

Numerical lattice QCD calculations using Monte Carlo methods can be extremely computationally intensive, requiring the use of the largest available supercomputers.

* Numerical integration using the Romberg algorithm

Numerical analysis using network simulation is often a less expensive approach.

Armscor is an ISO 9001 certified compliant company which manufactures weapons using CNC ( Computer Numerical Control ) equipment.

* NEC Lab is an antenna tool based on NEC ( Numerical Electromagnetics Code ) to analyze and design antenna using Artificial Intelligence, see ( Artificial intelligence )

Numerical optimization can be performed by a built-in tool, using COMPLEX or particle swarm algorithms.

* Simpson's 1 / 3rd rule of integration-Notes, PPT, Mathcad, Matlab, Mathematica, Maple at Numerical Methods for STEM undergraduate

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.

* Simpson's Rule for Numerical Integration

For computer savvy do-it-yourself hobbyists CNC ( Computer Numerical Control ) machining is also popular.

Identity, sometimes called Numerical Identity, is the relation that a " thing " bears to itself, and which no " thing " bears to anything other than itself ( cf.

Numerical Weather Prediction is a main focus in understanding air – sea interaction, tropical meteorology, atmospheric predictability, and tropospheric / stratospheric processes.

NOGAPS is run operationally at Fleet Numerical Meteorology and Oceanography Center for the United States Military.

Numerical analysis is the study of algorithms that use numerical approximation ( as opposed to general symbolic manipulations ) for the problems of mathematical analysis ( as distinguished from discrete mathematics ).

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.

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

** Assembly of the world's first general purpose electronic computer, the Electronic Numerical Integrator and Computer ( ENIAC ), is completed.

** ENIAC ( for " Electronic Numerical Integrator and Computer "), an early general-purpose electronic computer, is unveiled at the University of Pennsylvania.

Numerical aperture is commonly used in microscopy to describe the acceptance cone of an objective ( and hence its light-gathering ability and resolution ), and in fiber optics, in which it describes the cone of light accepted into the fiber or exiting it.

Numerical aperture is used to define the " pit size " in optical disc formats.

Numerical aperture is not typically used in photography.

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

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

* 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.

Numerical substitution of the above values gives the ideal gas approximation of sound velocity for gases, which is accurate at relatively low gas pressures and densities ( for air, this includes standard Earth sea-level conditions ).

Numerical root-finding methods use iteration, producing a sequence of numbers that hopefully converge towards a limit ( the so called " fixed point ") which is a root.

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.

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

Numerical sight-singing, an alternative to the solfege system of sight-singing, is a musical notation system that numbers the diatonic scale with the numbers one through eight ( or, alternately, one to seven, with the octave again being one ).

Numerical sight singing is not the same as integer notation derived from musical set theory and used primarily for sight singing atonal music.

Numerical ordinary differential equations is the part of numerical analysis which studies the numerical solution of ordinary differential equations ( ODEs ).

The effective Numerical Aperture of such assembly is usually not enough to allow for a full 3D optical trap but only for a 2D trap ( optical trapping and manipulation of objects will be possible only when, e. g., they are in contact with a surface ).