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Manuscript Title: A REDUCE package for finding conserved densities of systems of implicit difference-difference equations
Authors: Min Gao, Yasuyuki Kato, Masaaki Ito
Program title: TXCD
Catalogue identifier: ADTS_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 160(2004)69
Programming language: REDUCE 3.6, RLISP.
Computer: PC/AT compatible machine.
Operating system: Windows 2000.
RAM: Depends on the problem, minimum about 2 M bytes.
Word size: 32
Keywords: Conserved density, Implicit difference-difference equation, Computer algebra, REDUCE.
PACS: 02.70.Rw, 02.90.+p..
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 difference-difference equations which can be transformed to polynomial ones, and determine the homogeneous conservation laws.

Running time:
It depends on the equation and the rank of the conserved density. It increases exponentially with the rank of the conserved density. The running times on the PC Pentium with operating systems Windows 2000 (Xeon, 1.7 GHz) are shown in the table below. Timings are given in milliseconds.
Performance on Windows

Example

Rank

0

1

2

3

4

5

6

7

8

9

1(i)

15

15

15

31

150

718

5483

28176

127914

493092

1(ii)

15

15

16

63

170

2264

11171

103938

299001

1386468

1(iii)

15

15

15

46

250

5686

29210

203190

924372

1(iv)

15

15

15

31

47

156

1031

8905

40485

194595

2

15

15

45

187

2358

36673

433794

3(i)

15

63

1780

66518

1390030

**

3(ii)

15

47

829

37640

786594

**

The cases ** were rejected by memory error.