THE STABILITY OF THE THETA-METHODS IN THE NUMERICAL-SOLUTION OF DELAY DIFFERENTIAL-EQUATIONS

This paper deals with the stability analysis of numerical methods for the solution of delay differential equations. We focus on the behaviour of the one-leg θ-method and the linear θ-method in the solution of the linear test equation U'(t)=λU(t)+μU(t - τ), with τ>0 and complex λ,μ The stability regions for both of these methods are determined. The regions turn out to be equal to each other only if θ=0 or θ=1. © 1989 Oxford University Press.