: the quality, state, or degree of being stable <emotional stability><chemical stability>
In mathematics, a condition in which a slight disturbance in a system does not produce a significant disrupting effect on that system. A solution to a differential equation is said to be stable if a slightly different solution that is close to it when x = 0 remains close for nearby values of x. Stability of solutions is important in physical applications because deviations in mathematical models inevitably result from errors in measurement. A stable solution will be usable despite such deviations.