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Manuscript Title: A REDUCE package for finding conserved densities of systems of nonlinear difference-difference equations.
Authors: M. Gao, Y. Kato, M. Ito
Program title: FDCD
Catalogue identifier: ADQJ_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 148(2002)242
Programming language: Reduce 3.6, Rlisp.
Computer: PC/AT compatible machine.
Operating system: Windows 2000, FreeBSD.
RAM: 2M words
Word size: 32
Keywords: Conserved density, Finite difference equations, Computer algebra, REDUCE.
Classification: 5.

Nature of problem:
The existence of conserved densities for difference-difference equations is of interest for their classification and for understanding the stability of their solutions.

Restrictions:
The program can handle explicit difference-difference equations and nonlinear difference equations which can be transformed to polynomial ones.

Running time:
It depends on the equation and the rank of the conserved density. It increases exponentially with the rank of the conserved density. Table 1 shows the running times on the PC Pentium with operating systems Windows 2000 (Pentium III, 600MHz) and FreeBSD (Pentium 4, 2GHz). Timings are given in milliseconds.
Table 1. Performance on Windows (FreeBSD)
                              
 ------------------------------------------------------------------------
         |                            rank                               
 example |---------------------------------------------------------------
         |   1    |    2    |       3      |       4         |   >=5     
 --------|--------|---------|--------------|-----------------|-----------
    1    | 10 (1) |  20 (2) |      80 (27) |    1715655 (**) | ** (**)   
         |        |         |              |                 |           
    2    | 10 (1) |  20 (5) |  2033 (3630) |         ** (**) | ** (**)   
         |        |         |              |                 |           
    3    | 10 (1) |  20 (5) |     180 (53) |   33308 (50569) | ** (**)   
 ------------------------------------------------------------------------
The cases ** were rejected by memory error.