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COSY Infinity and its Applications to Nonlinear Dynamics

Abstract

The Fortran-based environment COSY INFINTIY, 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, quantitativ and mathematically rigorous statemen 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 beamphysics for the study and design of particle accelerators.

M. Berz, K. Makino, K. Shamseddine, G. Hoffstätter, W. Wan, in: "Computational Differentiation: Techniques, Applications, and Tools", M. Berz, C. Bischof, G. Corliss, A. Griewank (Eds.) (1996) 363-367, SIAM

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