# Stability

From AMS Glossary

(Redirected from Numerical instability)

## stability

- The characteristic of a system if sufficiently small disturbances have only small effects, either decreasing in amplitude or oscillating periodically; it is asymptotically stable if the effect of small disturbances vanishes for long time periods.

A system that is not stable is referred to as unstable, for which small disturbances may lead to large effects. Some authors also distinguish a neutral or marginally stable case, in which disturbances do not vanish, but also do not grow without bound. Classically, stability was defined only with respect to systems in equilibrium. More recently it has been extended to apply to evolving systems, for which an unstable disturbance leads to an evolution that becomes uncorrelated with the undisturbed evolution. From this standpoint stability and predictability can be equated.

- The property that each computed solution (in exact arithmetic) of a finite difference approximation remains bounded for all possible choices of the time step.

- The ability of laminar flow to become turbulent in a fluid.