The Stability of the $θ$-Methods for Delay Differential Equations (Journal of Computational Mathematics, 1999)
This paper deals with the stability analysis of numerical methods for the solution of delay differential equations. We focus on the behaviour of three $θ$-methods in the solution of the linear test equation $u'(t)=A(t)u(t)+B(t)u(τ(t))$ with $τ(t)$ and $A(t), B(t)$ continuous matrix functions. The stability regions for the three $θ$-methods are determined.