In
computational mathematics
Computational mathematics is an area of mathematics devoted to the interaction between mathematics and computer computation.National Science Foundation, Division of Mathematical ScienceProgram description PD 06-888 Computational Mathematics 2006 ...
, numerical dispersion is a difficulty with computer simulations of continua (such as fluids) wherein the simulated medium exhibits a higher dispersivity than the true medium. This phenomenon can be particularly egregious when the system should not be dispersive at all, for example a fluid acquiring some spurious dispersion in a numerical model.
It occurs whenever the
dispersion relation
In the physical sciences and electrical engineering, dispersion relations describe the effect of dispersion on the properties of waves in a medium. A dispersion relation relates the wavelength or wavenumber of a wave to its frequency. Given the d ...
for the finite difference approximation is nonlinear. For these reasons, it is often seen as a
numerical error In software engineering and mathematics, numerical error is the error in the numerical computations.
Types
It can be the combined effect of two kinds of error in a calculation.
* the first is caused by the finite precision of computations involvi ...
.
Numerical dispersion is often identified, linked and compared with
numerical diffusion
Numerical diffusion is a difficulty with computer simulations of continua (such as fluids) wherein the simulated medium exhibits a higher diffusivity than the true medium. This phenomenon can be particularly egregious when the system should not be ...
, another
artifact of similar origin.
Explanation
In simulations, time and space are divided into discrete grids and the continuous differential equations of motion (such as the Navier–Stokes equation) are discretized into finite-difference equations;
these discrete equations are in general unidentical to the original differential equations, so the simulated system behaves differently than the intended physical system. The amount and character of the difference depends on the system being simulated and the type of discretization that is used.
See also
*
Numerical diffusion
Numerical diffusion is a difficulty with computer simulations of continua (such as fluids) wherein the simulated medium exhibits a higher diffusivity than the true medium. This phenomenon can be particularly egregious when the system should not be ...
*
Von Neumann stability analysis
The term ''von'' () is used in German language surnames either as a nobiliary particle indicating a noble patrilineality, or as a simple preposition used by commoners that means ''of'' or ''from''.
Nobility directories like the ''Almanach de Go ...
References
dispersion
Dispersion may refer to:
Economics and finance
*Dispersion (finance), a measure for the statistical distribution of portfolio returns
*Price dispersion, a variation in prices across sellers of the same item
*Wage dispersion, the amount of variatio ...
Numerical differential equations
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