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**Asymptotic stability of linear delay differential-algebraic equations and numerical methods.**
*(English)*
Zbl 0879.65060

Delay differential-algebraic equations which have both delay and algebraic constraints appear frequently in various fields like chemical process simulations. Not much work has been done on numerical methods for these equations. Since 1990 in some papers the structure of those equations as well as order and convergence of some numerical methods have been studied, but little is known about asymptotic stability of systems of this kind.

The paper under review is devoted to studying asymptotic stability of numerical methods for linear constant coefficient delay differential-algebraic equations. The authors discuss \(\theta\)-methods, multistep methods and Runge-Kutta methods. In an anounced subsequent paper the authors will present stability results for nonlinear delay differential-algebraic equations.

The paper under review is devoted to studying asymptotic stability of numerical methods for linear constant coefficient delay differential-algebraic equations. The authors discuss \(\theta\)-methods, multistep methods and Runge-Kutta methods. In an anounced subsequent paper the authors will present stability results for nonlinear delay differential-algebraic equations.

Reviewer: H.Ade (Mainz)

### MSC:

65L20 | Stability and convergence of numerical methods for ordinary differential equations |

34K05 | General theory of functional-differential equations |

34A09 | Implicit ordinary differential equations, differential-algebraic equations |

65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |

65L05 | Numerical methods for initial value problems involving ordinary differential equations |

### Keywords:

theta methods; delay differential-algebraic equations; asymptotic stability; multistep methods; Runge-Kutta methods### Software:

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\textit{W. Zhu} and \textit{L. R. Petzold}, Appl. Numer. Math. 24, No. 2--3, 247--264 (1997; Zbl 0879.65060)

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### References:

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