Numerical simulations have suggested that the eventual formation of a perihelion secular resonance between Mercury and Jupiter ( g < sub > 1 </ sub >= g < sub > 5 </ sub >) has the potential to greatly increase Mercury's eccentricity and possibly destabilize the inner Solar System several billion years from now.

Numerical simulations suggest that the orbits of plutinos with an eccentricity 10 %– 30 % smaller or larger than that of Pluto are not stable over Ga timescales.

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.

* Computational physics – Numerical simulations of large non-analytic systems

Numerical simulations based on CDM gave predictions of the shape of the rotation curves in the centre of dark-matter dominated systems, such as these galaxies.

Numerical simulations of vortex tangles, basis for vortex reconnexions, connexions between bundles recently investigated.

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 simulations show that there is a 0. 41 probability that the moon Halimede collided with Nereid at some time in the past.

Numerical simulations have shown that under proper conditions it is possible to build up an oxygen atmosphere via photolysis of carbon dioxide.

Numerical simulations of two-dimensional magnetic reconnection typically show agreement with this model.

Numerical simulations confirmed the experimental observations, and further showed that the observed vector solitons are the two types of phase-locked polarization domain-wall solitons theoretically predicted.

Numerical simulations have different objectives depending on the nature of the task being simulated:

* Efstathiou G., Davis M., White S. D. M., Frenk C. S., " Numerical techniques for large cosmological N-body simulations ", 1985, ApJ.

Numerical simulations of the collision that created the Eos family suggest that the smaller body was about a tenth the mass of the parent and struck from a direction out of the ecliptic plane.

Numerical analysis textbooks give formulas for the condition numbers of problems and identify the backward stable algorithms.

* Masi D. M. B., Fischer M. J., Harris C. M., Numerical Analysis of Routing Rules for Call centres, Telecommunications Review, 1998, noblis. org

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.

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 ).

( See " Seneca-A Language for Numerical Applications on Vectorcomputers ", Proc CONPAR 90-VAPP IV Conf.

Numerical determination of rank requires a criterion for deciding when a value, such as a singular value from the SVD, should be treated as zero, a practical choice which depends on both the matrix and the application.

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

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

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

Numerical calculation of the integral using the trapezoidal rule or Simpson's rule is not efficient and becomes numerically unstable especially for configurations with large Fresnel number.

* Numerical analysis, the study of algorithms for approximating the problems of continuous mathematics.

* A. Bobet, A. Fakhimi, S. Johnson, J. Morris, F. Tonon, and M. Ronald Yeung ( 2009 ) " Numerical Models in Discontinuous Media: Review of Advances for Rock Mechanics Applications ", J. Geotech.

* 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 analysis takes advantage of many of the properties of orthogonal matrices for numerical linear algebra, and they arise naturally.

It was named in honor of von Neumann, short for John v. Neumann Numerical Integrator and Automatic Computer.

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 integration consists of finding numerical approximations for the value

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 computational geometry, also called machine geometry, computer-aided geometric design ( CAGD ), or geometric modeling, which deals primarily with representing real-world objects in forms suitable for computer computations in CAD / CAM systems.

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.

See Numerical approximations of π for more on the history.

* John Hull and Alan White, " Numerical procedures for implementing term structure models I ," Journal of Derivatives, Fall 1994, pp 7 – 16

* John Hull and Alan White, " Numerical procedures for implementing term structure models II ," Journal of Derivatives, Winter 1994, pp 37 – 48

Numerical abnormalities, also known as aneuploidy, often occur as a result of nondisjunction during meiosis in the formation of a gamete ; trisomies, in which three copies of a chromosome are present instead of the usual two, are common numerical abnormalities.

Numerical weather prediction uses mathematical models of the atmosphere and oceans to predict the weather based on current weather conditions.

Numerical calculations and some other arguments have also hinted at this possibility.

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.

With his Los Alamos colleague Robert Schrandt he published a report, " Some Elementary Attempts at Numerical Modeling of Problems Concerning Rates of Evolutionary Processes ", which applied some of his earlier ideas on branching processes to biological inheritance.

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 digits are not allowed but are used in some databases to indicate the position in the sequence.

Early criticism centered on the books ' assumed unreliability ( the First Edition indeed contained some mistakes ), the exclusion of some algorithms, and the authors ' implication, not always correct, that their programs were as efficient and reliable as " black-box " libraries, for example the NAG Numerical Libraries.