by Alan K. Head CSIRO Division of Materials Science and Technology Melbourne Australia Postal: Private Bag 33 Note new postal as of 1/1/94 Rosebank MDC Clayton, Vic 3169 Australia Phone: (03) 542 2861 Fax: (03) 544 1128 E-mail: firstname.lastname@example.org Equipment --------- Any IBM type PC with at least 256k of free memory. Any version of DOS. An attached printer is very useful. Availability ------------ By anonymous ftp at oak.oakland.edu, SIMTEL or wurchive.wustl.edu The current version is 4.4. Improvements over the previous version are significant: * Lie-Backlund symmetries added to Point and Contact symmetries. * Improvements to speed and effective size of workspace. * Extended coverage of differential equations containing arbitrary symbolic functions. * Extended coverage of non-classical symmetries that involve use of the invariant surface condition and lead to non-linear Lie determining equations. Literature ----------- A.K. Head, "LIE, a PC program for Lie analysis of differential equations", Computer Physics Communications, vol 71 (1993) pp 241-248. Description ----------- Lie analysis is the only systematic method of finding exact solutions of differential equations, ordinary or partial, a single equation or a set of equations. It involves a large amount of symbolic calculation that is better done by computer. LIE is a self-contained stand-alone package to do this on any PC. It comes with instruction files (with updates in a README), source code, test run and a number of examples of differential equation input data files, some well known in the literature and some new.
LIE is written in MUMATH, the symbolic mathematics language for IBM type PCs. Previous versions have required you to have the MUMATH system. By generous permission of Soft Warehouse Inc, authors and owners of MUMATH, this is no longer necessary. A limited version of MUMATH is combined with LIE to give MULIE.EXE which is a complete stand-alone operating program. LIE calculates and solves the determining equations automatically for single equations and systems of differential equations. LIE also computes the Lie vectors and their commutators.