Computer Physics Communications Program Library

Programs in Physics & Physical Chemistry

PROGRAM SUMMARY

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

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.