Differential algebraic equations with after-effect.

*(English)*Zbl 0996.65077Summary: We are concerned with the solution of delay differential algebraic equations. These are differential algebraic equations with after-effect, or constrained delay differential equations. The general semi-explicit form of the problem consists of a set of delay differential equations combined with a set of constraints that may involve retarded arguments. Even simply stated problems of this type can give rise to difficult analytical and numerical problems. The more tractable examples can be shown to be equivalent to systems of delay or neutral delay differential equations. Our purpose is to highlight some of the complexities and obstacles that can arise when solving these problems, and to indicate problems that require further research.

##### MSC:

65L80 | Numerical methods for differential-algebraic equations |

34E15 | Singular perturbations, general theory for ordinary differential equations |

65L05 | Numerical methods for initial value problems |

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

34K28 | Numerical approximation of solutions of functional-differential equations (MSC2010) |

##### Keywords:

index reduction; singular perturbation; delay differential algebraic equations; neutral delay differential equations##### Software:

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\textit{C. T. H. Baker} et al., J. Comput. Appl. Math. 140, No. 1--2, 63--80 (2002; Zbl 0996.65077)

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