# Index Determination of DAEs—A Wide Field for Automatic Differentiation

@inproceedings{Lamour2009IndexDO, title={Index Determination of DAEs—A Wide Field for Automatic Differentiation}, author={Ren{\'e} Lamour and Dagmar Monett}, year={2009} }

The index of a Differential‐Algebraic equation (DAE) describes the expected difficulties solving such an equation. The tractability index bases on a linearization of the DAE along a given trajectory. Using these Jacobian matrices of the linearization the termination of a matrix sequence determines the index of the DAE. Because of the drawbacks of symbolic differentiation, numerical differentiation, and differentiation by hand we use for the necessary differentiations the Algorithmic… Expand

#### 5 Citations

Projector based integration of DAEs with the Taylor series method using automatic differentiation

- Computer Science, Mathematics
- J. Comput. Appl. Math.
- 2014

A new approach to compute consistent initial values and integrate DAEs up to index two, considering the nonlinear DAE in each time-step as a nonlinear system of equations for Taylor expansions. Expand

A new algorithm for the index determination in DAEs by Taylor series using Algorithmic Differentiation

- Mathematics
- 2010

We present an approach for determining the tractability index using truncated polynomial arithmetic. In particular, computing the index this way generates a sequence of matrices that contains itself… Expand

InitDAE: Computation of consistent values, index determination and diagnosis of singularities of DAEs using automatic differentiation in Python

- Computer Science, Mathematics
- J. Comput. Appl. Math.
- 2021

An overview of the InitDAE algorithm is given, actual features are shown, future possibilities are discussed and future possibilities, in particular the integration with Taylor series methods are discussed. Expand

A new algorithm for index determination in DAEs using algorithmic differentiation

- Mathematics, Computer Science
- Numerical Algorithms
- 2011

An approach for determining the tractability index using truncated polynomial arithmetic, which generates a sequence of matrices that contains itself derivatives, and implements the time differentiations using algorithmic differentiation techniques. Expand

Differential-algebraic Equations with regular local matrix pencils

- Mathematics
- 2013

In the projector based framework, any regular linear DAE features several continuous time-varying characteristic subspaces that are independent of construction technicalities, among them the… Expand

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