This paper focuses on the numerical stability of the block θ methods adapted to differential equations with a delay argument. For the block θ methods, an interpolation procedure is introduced which leads to the numerical processes that satisfy an important asymptotic stability condition related to the class of test problems y′(t)=ay(t)+by(t-τ) with a,b∈C, Re(a)0. We prove that the block θ method is GP stable if and only if the method is A stable for ordinary differential equations. Furthermore, it is proved that the P and GP stability are equivalent for the block θ method.
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