Overview

Digital computers are used extensively in the analysis of dynamical systems. The equations describing the motion of a system are partly dynamic and partly kinematic in nature. In either case, they take the form of ordinary differential equations which are nonlinear, in general. These differential equations are usually written with time as the independent variable, and time is assumed to vary in a continuous manner from some initial value, frequently zero, to a final value.

In any representation using digital computers, the time can assume only a finite number of discrete values. The differential equations of the system are replaced by difference equations. The solutions of these difference equations are not the same, in general, as the solutions of the corresponding differential equations at the given discrete times, thereby introducing computational errors. More importantly, if parameters such as step size are not properly chosen, a given numerical procedure may produce an apparent unstable response for a system that is actually stable.