Abstract
We give an overview of the theory of unstructured nonlinear DAEs of arbitrary index. The approach is extended to overdetermined consistent DAEs in order to be able to include known first integrals. We then discuss various computational issues for the numerical solution of corresponding DAE problems. These include the design of special Gaus-Newton techniques as well as the treatment of parametrized nonlinear systems in the context of DAEs. Examples demonstrate their applicability and performance.
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