On the asymptotic stability ofθ-methods for delay differential equations

SummaryStability regions of θ-methods for the linear delay differential test equations $$\begin{gathered} y'(t) = py(t) + qy(t - \tau ),t > 0, \hfill \\ y(t) = \varphi (t),t \in [ - \tau ,0], \hfill \\ \end{gathered}$$ where τ is a positive constant, are presented. In the case thatp andq are real constant coefficients, necessary and sufficient conditions on the stepsize for the stability of a θ-method are obtained. Furthermore, whenp andq are complex coefficients, sufficient conditions for the stability of the θ-methods are also given.

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