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 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.