Numerical instability

Numerical instability deals with an unexpected phenomenon which arises from the numerical solution of ordinary or partial differential equations. The usual notion of instability includes concepts such as fickleness, unreliability, and oversensitivity. If a computation is numerically unstable it gives inaccurate results. A major source of numerical instability results from a multiplicative magnification effect of small unavoidable errors on the numerical results. Detailed analysis of difference schemes are used to determine, in advance, whether a proposed solution will give stable computational results.

For more, but confusing and inaccurate, discussion see numerical stability here on wiki. A search on Google for "numerical instability" might be helpful. The basic phenomenon is instability.

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