The authors’ approach to the solution of a system of partial differential equations is based on the concept of equation symmetry. This concept was initially developed by Lie. It was later expanded and successfully employed by Ames, Harrison and Estabrook, and Stephani.

The authors have implemented the Lie symmetry concept and the Harrison-Estabrook procedure using a MAPLE symbolic computing system. In this paper, the resulting algorithms, subroutines, and interactive tools are presented. As examples of the application, they discuss the Boltzmann equation, the Korteweg-deVries equation, fluid dynamics, and magneto-hydrodynamics. The paper is written clearly, but a working knowledge of MAPLE is required.