Differential Equation Solvers & Tools


PDELIE is a Macsyma package developed by Peter Vafeades from Trinity University. It comes with Macsyma in the share library.

This package analyzes differential equation systems using Lie symmetry group methods. The analysis starts by determining the symmetry vectorfields for the particular differential system, be they geometric or of Bessel-Haagen type. The user may then compute structure constants for Lie subalgebras generated by the symmetry vectorfields. Lie algebras or subalgebras may then be used to reduce the differential system to one involving fewer dependent and independent variables. This usually leads to either an ordinary differential equation or an algebraic system. The reduced equations sometimes can be solved to give explicit symbolic solutions for the original system of equations. When the system is variational, the user may compute the Noether conservation laws of the system.



Work in Progress

Boundary Value Problems may be solved through Lie symmetry group methods. In the case of linear systems, superposition makes this task easier; for nonlinear systems, however, the differential system as well as the boundary conditions and boundary of the domain must share the same symmetries. Since this restriction is so severe, it would be useful if the package could suggest the type of boundary conditions and the shape of domains in which similarity solutions computed by PL_SOLVE would be valid.
Special Purpose Systems

Last updated: November 15, 1994