Differential algebraic equations with after-effect

Authors:
C. T. H. Baker;C. A. H. Paul;H. Tian
Affiliations:
Department of Mathematics, The University of Manchester, Oxford Road, Manchester, UK;Department of Mathematics, The University of Manchester, Oxford Road, Manchester, UK;Department of Mathematics, The University of Manchester, Oxford Road, Manchester, UK
Venue:
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 9th International Congress on computational and applied mathematics
Year:
2002

Citing 11
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Abstract

In this paper, 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.