BibTeX
@INCOLLECTION{
         Feehery1996ADB,
       author = "William F. Feehery and Paul I. Barton",
       editor = "Martin Berz and Christian Bischof and George Corliss and Andreas Griewank",
       title = "A Differentiation-Based Approach to Dynamic Simulation and Optimization with
         High-Index Differential-Algebraic Equations",
       booktitle = "Computational Differentiation: Techniques, Applications, and Tools",
       pages = "239--252",
       publisher = "SIAM",
       address = "Philadelphia, PA",
       key = "Feehery1996ADB",
       crossref = "Berz1996CDT",
       abstract = "Reliable methods for solving simulation and dynamic optimization problems must be
         able to handle the high-index DAEs that arise naturally in these problems. This paper details a
         modified and automated version of the method of dummy derivatives for solving high-index DAEs that
         has been implemented within the ABACUSS large-scale equation based modeling environment. To
         implement our algorithm, we have developed a method for ``dummy variable pivoting'' into a
         standard DAE solver. Our approach requires a hybrid symbolic and numeric strategy in which we apply
         computational differentiation to the high-index system, and then employ a numerical integrator to
         solve the resulting index-1 system. We have modified the dummy derivative method for solving
         high-index DAEs in several ways to reduce the computational cost required to select and pivot the
         dummy derivative set. This work demonstrates the feasibility and desirability of using a hybrid
         numerical and symbolic strategy for the solution of certain classes of simulation and dynamic
         optimization problems.",
       keywords = "Simulation, dynamic optimization, high-index DAEs, dummy derivatives, ABACUSS.",
       referred = "[Pusch1996JSa].",
       year = "1996"
}