This paper presents the cause of instabilities which arise during the numerical solution of ordinary differential equations. By using the numerical integration routines presently available, one actually approximates the differential equation by a difference equation. If the difference equation is of a higher order than the original differential equation, the approximate solution contains extraneous solutions which are not at all related to the true solution. It is the behavior of these extraneous solutions that one is usually concerned with in a stability analysis.
Also presented is a procedure for obtaining a bound on the largest allowable integration step size for a class of chemical engineering problems. A detailed explanation of the procedure is illustrated for unsteady state distillation calculations.