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 continuum limits. Solutions with definite transformation properties are obtained; identities and formulas for these functions are then derived using the symmetry algebra.

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