LIE SYMMETRIES OF FINITE-DIFFERENCE EQUATIONS

Discretizations of the Helmholtz, heat, and wave equations on uniform lattices are considered in various space-time dimensions. The symmetry properties of these finite-difference equations are determined and it is found that they retain the same Lie symmetry algebras as their con tinuum limits. Solutions with definite transformation properties are o btained; identities and formulas for these functions are then derived using the symmetry algebra. (C) 1995 American Institute of Physics.