Publication: COSY INFINITY and Its Applications in Nonlinear Dynamics
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COSY INFINITY and Its Applications in Nonlinear Dynamics

- incollection -
 

Author(s)
Martin Berz , Kyoko Makino , Khodr Shamseddine , Georg H. Hoffstätter , Weishi Wan

Published in
Computational Differentiation: Techniques, Applications, and Tools

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

Year
1996

Publisher
SIAM

Abstract
The Fortran-based environment COSY INFINITY, as well as the related codes DAFOR and DAPRE, is presented. The codes contain modules for the computation of derivatives to very high orders in many variables, with a particular emphasis on sparsity. The main use of the code lies in the field of nonlinear dynamics, where it is used for the computation of perturbation expansions of Poincare maps to high orders as well as their analysis based on normal forms and other methods. Using Remainder Differential Algebraic Methods, quantitative and mathematically rigorous statements about long-term stability can be made for general systems. The code is currently used by more than 150 registered users, mostly in the field of beam physics for the study and design of particle accelerators.

Cross-References
Berz1996CDT

AD Tools
COSY INFINITY

AD Theory and Techniques
Sparsity

BibTeX
@INCOLLECTION{
         Berz1996CIa,
       author = "Martin Berz and Kyoko Makino and Khodr Shamseddine and Georg H.
         Hoffst{\"a}tter and Weishi Wan",
       editor = "Martin Berz and Christian Bischof and George Corliss and Andreas Griewank",
       title = "{COSY INFINITY} and Its Applications in Nonlinear Dynamics",
       booktitle = "Computational Differentiation: Techniques, Applications, and Tools",
       pages = "363--365",
       publisher = "SIAM",
       address = "Philadelphia, PA",
       key = "Berz1996CIa",
       crossref = "Berz1996CDT",
       abstract = "The Fortran-based environment COSY INFINITY, as well as the related codes DAFOR and
         DAPRE, is presented. The codes contain modules for the computation of derivatives to very high
         orders in many variables, with a particular emphasis on sparsity. The main use of the code lies in
         the field of nonlinear dynamics, where it is used for the computation of perturbation expansions of
         Poincare maps to high orders as well as their analysis based on normal forms and other methods.
         Using Remainder Differential Algebraic Methods, quantitative and mathematically rigorous statements
         about long-term stability can be made for general systems. The code is currently used by more than
         150 registered users, mostly in the field of beam physics for the study and design of particle
         accelerators.",
       keywords = "COSY INFINITY, high-order derivatives, sparsity, nonlinear dynamics, differential
         algebra.",
       referred = "[Fuchi1996a], [Hoefkens2001EHO], [Kearfott2002TMi], [Makino2002NAo],
         [Shamseddine1996EHi].",
       year = "1996",
       ad_tools = "COSY INFINITY",
       ad_theotech = "Sparsity"
}


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