(untitled) (Journal of Computational Mathematics, 1996)
This paper deals with the stability analysis of θ -methods for the numerical solution of delay differential equations (DDEs). We focus on the behaviour of such methods in the solution of the linear test equation y^′(t)=a(t)y(t)+b(t)y(t-τ ), where τ >0, a(t) and b(t) are functions from R to C. It is proved that the linear θ -method and the one-leg θ -method are TGP-stable if and only if θ =1.