Differential Equation Solvers & Tools

Program LIE for Lie analysis of differential equations on IBM type PCs

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
Phone: (03) 542 2861
Fax: (03) 544 1128

Any IBM type PC with at least 256k of free memory.
Any version of DOS. An attached printer is very useful.

By anonymous ftp at, SIMTEL or
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. 

A.K. Head, "LIE, a PC program for Lie analysis of differential equations",
Computer Physics Communications, vol 71  (1993)  pp 241-248.

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.

Special Purpose Systems

Last updated: November 15, 1994