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On the asymptotic stability ofθ-methods for delay differential equations

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Summary

Stability 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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  1. Departamento de Matemática Aplicada, Facultad de Ciencias, E-50009, Zaragoza, Spain

    M. Calvo & T. Grande

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  1. M. Calvo
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  2. T. Grande
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Calvo, M., Grande, T. On the asymptotic stability ofθ-methods for delay differential equations. Numer. Math. 54, 257–269 (1989). https://doi.org/10.1007/BF01396761

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