STABILITY ANALYSIS OF NUMERICAL-METHODS FOR DELAY DIFFERENTIAL-EQUATIONS

This paper deals with the stability analysis of step-by-step methods for the numerical solution of delay differential equations. We focus on the behaviour of such methods when they are applied to the linear testproblem U'(t) = lambda-U(t) + mu-U(t - tau) with tau > 0 and lambda, mu-complex. A general theorem is presented which can be used to obtain complete characterizations of the stability regions of these methods.