Differential-algebraic equations: theory and simulation. (English) Zbl 1327.65151
Benner, Peter (ed.) et al., Numerical algebra, matrix theory, differential-algebraic equations and control theory. Festschrift in honor of Volker Mehrmann. Cham: Springer (ISBN 978-3-319-15259-2/hbk; 978-3-319-15260-8/ebook). 435-462 (2015).
Summary: 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 Gauß-Newton techniques as well as the treatment of parametrized nonlinear systems in the context of DAEs. Examples demonstrate their applicability and performance.
For the entire collection see [Zbl 1322.00048].
For the entire collection see [Zbl 1322.00048].
MSC:
| 65L80 | Numerical methods for differential-algebraic equations |
