Article | Proceedings of the 5th International Workshop on Equation-Based Object-Oriented Modeling Languages and Tools; April 19; University of Nottingham; Nottingham; UK | Simplification of Differential Algebraic Equations by the Projection Method
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Title:
Simplification of Differential Algebraic Equations by the Projection Method
Author:
Elena Shmoylova: Maplesoft, Canada Jürgen Gerhard: Maplesoft, Canada Erik Postma: Maplesoft, Canada Austin Roche: Maplesoft, Canada
Download:
Full text (pdf)
Year:
2013
Conference:
Proceedings of the 5th International Workshop on Equation-Based Object-Oriented Modeling Languages and Tools; April 19; University of Nottingham; Nottingham; UK
Issue:
084
Article no.:
010
Pages:
87-96
No. of pages:
10
Publication type:
Abstract and Fulltext
Published:
2013-03-27
ISBN:
978-91-7519-621-3 (print)
978-91-7519-617-6 (online)
Series:
Linköping Electronic Conference Proceedings
ISSN (print):
1650-3686
ISSN (online):
1650-3740
Publisher:
Linköping University Electronic Press; Linköpings universitet


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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.

Keywords: differential algebraic equations; index reduction; projection method

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

Author:
Elena Shmoylova, Jürgen Gerhard, Erik Postma, Austin Roche
Title:
Simplification of Differential Algebraic Equations by the Projection Method
References:

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

Author:
Elena Shmoylova, Jürgen Gerhard, Erik Postma, Austin Roche
Title:
Simplification of Differential Algebraic Equations by the Projection Method
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