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Differential algebraic equations with after-effect. (English) Zbl 0996.65077
Summary: 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.

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)
Full Text: DOI
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