LIE, a PC program for Lie analysis of differential equations Original Research Article

LIE is a self-contained PC program for the Lie analysis of ordinary or partial differential equations, either a single equation or a simultaneous set. It is written in the symbolic mathematics language MUMATH and will run on any PC. It comes as a complete program that incorporates the necessary parts of MUMATH and is ready to run. The previous version was for classical Lie analysis, finding the point symmetries of well-posed differential equations. This is now extended to contact, Lie-Backlund and nonclassical symmetries. Memory utilization has been improved and it can analyse the equations of Magneto-Hydrodynamics, a set of 9 partial differential equations in 12 variables.