Publication: Efficient High-Order Methods for ODEs and DAEs
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Efficient High-Order Methods for ODEs and DAEs

- incollection -
 

Author(s)
Jens Hoefkens , Martin Berz , Kyoko Makino

Published in
Automatic Differentiation of Algorithms: From Simulation to Optimization

Editor(s)
George Corliss, Christèle Faure, Andreas Griewank, Laurent Hascoët, Uwe Naumann

Year
2002

Publisher
Springer

Abstract
We present methods for the high-order differentiation through ordinary differential equations (ODEs), and more importantly, differential algebraic equations (DAEs). First, methods are developed that assert that the requested derivatives are really those of the solution of the ODE, and not those of the algorithm used to solve the ODE. Next, high-order solvers for DAEs are developed that in a fully automatic way turn an n-th order solution step of the DAEs into a corresponding step for an ODE initial value problem. In particular, this requires the automatic high-order solution of implicit relations, which is achieved using an iterative algorithm that converges to the exact result in at most n+1 steps. We give examples of the performance of the method.

Cross-References
Corliss2002ADo

BibTeX
@INCOLLECTION{
         Hoefkens2002EHO,
       author = "Jens Hoefkens and Martin Berz and Kyoko Makino",
       title = "Efficient High-Order Methods for {ODE}s and {DAE}s",
       pages = "343--348",
       abstract = "We present methods for the high-order differentiation through ordinary differential
         equations (ODEs), and more importantly, differential algebraic equations (DAEs). First, methods are
         developed that assert that the requested derivatives are really those of the solution of the ODE,
         and not those of the algorithm used to solve the ODE. Next, high-order solvers for DAEs are
         developed that in a fully automatic way turn an $n$-th order solution step of the DAEs into a
         corresponding step for an ODE initial value problem. In particular, this requires the automatic
         high-order solution of implicit relations, which is achieved using an iterative algorithm that
         converges to the exact result in at most $n+1$ steps. We give examples of the performance of the
         method.",
       chapter = "41",
       crossref = "Corliss2002ADo",
       booktitle = "Automatic Differentiation of Algorithms: From Simulation to Optimization",
       year = "2002",
       editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent
         Hasco{\"e}t and Uwe Naumann",
       series = "Computer and Information Science",
       publisher = "Springer",
       address = "New York, NY"
}


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