Prognostic equation - in the context of physical (and especially geophysical) simulation, a prognostic equation predicts the value of variables for some time in the future on the basis of the values at the current or previous times.

For instance, the well-known Navier-Stokes equations that describe the time evolution of a fluid are prognostic equations that predict the future distribution of velocities in that fluid on the basis of current fields such as the pressure gradient.

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References

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James R. Holton (2004) An Introduction to Dynamic Meteorology, Academic Press, International Geophysics Series Volume 88, Fourth Edition, 535 p., ISBN 0-12-354015-1, ISBN 978-0-12-354015-7.

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http://glossary.ametsoc.org/wiki/Prognostic_equation