Conference article

Simplification of Differential Algebraic Equations by the Projection Method

Elena Shmoylova
Maplesoft, Canada

Jürgen Gerhard
Maplesoft, Canada

Erik Postma
Maplesoft, Canada

Austin Roche
Maplesoft, Canada

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Published in: Proceedings of the 5th International Workshop on Equation-Based Object-Oriented Modeling Languages and Tools; April 19; University of Nottingham; Nottingham; UK

Linköping Electronic Conference Proceedings 84:10, p. 87-96

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Published: 2013-03-27

ISBN: 978-91-7519-621-3 (print)

ISSN: 1650-3686 (print), 1650-3740 (online)


Reduction of a differential algebraic equation (DAE) system to an ordinary differential equation system (ODE) is an important step in solving the DAE numerically. When the ODE is obtained; an ODE solution technique can be used to obtain the final solution. In this paper we consider combining index reduction with projection onto the constraint manifold.We show that the reduction benefits from the projection for DAEs of certain form. We demonstrate that one of the applications where DAEs of this form appear is optimization under constraints. We emphasize the importance of optimization problems in physical systems and provide an example application of the projection method to an electric circuit formulated as an optimization problem where Kirchhoff’s laws are acting as constraints.


differential algebraic equations; index reduction; projection method


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