A REDUCE package for finding conserved densities of systems of implicit difference-difference equations

A computer algebra program for finding polynomial conserved densities of implicit difference-difference equations is presented. The algorithm is based on scaling properties and implemented in computer algebra system REDUCE. The package is applicable to systems of any number of nonlinear difference-difference equations of polynomial type.

Program summary

Title of program: TXCDCatalogue identifier: ADTSProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADTSProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandComputers: PC/AT compatible machineOperating systems: Windows 2000Programming language used: REDUCE 3.6, RLISPMemory required to execute with typical data: Depends on the problem, minimum about 2 M bytes.No. of bits in a word: 32No. of bytes in distributed program, including test data, etc.: 10 005No. of lines in distributed program, including test data, etc.: 1739Distribution format: tar gzip fileNature of physical problem: The existence of conserved densities for difference-difference equations is of interest for their classification and for understanding the stability of their solutions.Restriction on the complexity of the problem: The program can handle difference-difference equations which can be transformed to polynomial ones, and determine the homogeneous conservation laws.Typical 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.

Full-size table