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Automatic Differentiation and Implicit Differential Equations

- incollection -
 

Author(s)
Stephen L. Campbell , Richard Hollenbeck

Published in
Computational Differentiation: Techniques, Applications, and Tools

Editor(s)
Martin Berz, Christian Bischof, George Corliss, Andreas Griewank

Year
1996

Publisher
SIAM

Abstract
Many physical processes are most naturally and easily modeled as mixed systems of differential and algebraic equations (DAEs). There has been an increased interest in several areas in exploiting the advantages of working directly with these implicit models. Differentiation plays an important role in both the analysis and numerical solution of DAEs. Automatic differentiation can have a significant impact on what is considered a practical approach and what types of problems can be solved. However, working with DAEs places special demands on automatic differentiation codes. More is required than just computing a gradient quickly. This paper will begin with a brief introduction to DAEs and how differentiation is important when working with DAEs. Then the requirements in terms of both information and performance that DAEs make of automatic differentiation software will be presented. Some of our own experience in using automatic differentiation software will be mentioned. It will be seen that automatic differentiation software has a significant role to play in the future for DAEs but that not all of the demands that the numerical solution of DAEs places on automatic differentiation software are currently being met.

Cross-References
Berz1996CDT

BibTeX
@INCOLLECTION{
         Campbell1996ADa,
       author = "Stephen L. Campbell and Richard Hollenbeck",
       editor = "Martin Berz and Christian Bischof and George Corliss and Andreas Griewank",
       title = "Automatic Differentiation and Implicit Differential Equations",
       booktitle = "Computational Differentiation: Techniques, Applications, and Tools",
       pages = "215--227",
       publisher = "SIAM",
       address = "Philadelphia, PA",
       key = "Campbell1996ADa",
       crossref = "Berz1996CDT",
       abstract = "Many physical processes are most naturally and easily modeled as mixed systems of
         differential and algebraic equations (DAEs). There has been an increased interest in several areas
         in exploiting the advantages of working directly with these implicit models. Differentiation plays
         an important role in both the analysis and numerical solution of DAEs. Automatic differentiation can
         have a significant impact on what is considered a practical approach and what types of problems can
         be solved. However, working with DAEs places special demands on automatic differentiation codes.
         More is required than just computing a gradient quickly. This paper will begin with a brief
         introduction to DAEs and how differentiation is important when working with DAEs. Then the
         requirements in terms of both information and performance that DAEs make of automatic
         differentiation software will be presented. Some of our own experience in using automatic
         differentiation software will be mentioned. It will be seen that automatic differentiation software
         has a significant role to play in the future for DAEs but that not all of the demands that the
         numerical solution of DAEs places on automatic differentiation software are currently being met.",
       keywords = "Differential algebraic equations, numerical integrators, higher derivatives.",
       year = "1996"
}


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