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We show that any first order ordinary differential equation with a known Liepoint symmetry group can be discretized into a difference scheme with the samesymmetry group. In general, the lattices are not regular ones, but must beadapted to the symmetries considered. The invariant difference schemes can beso chosen that their solutions coincide exactly with those of the originaldifferential equation.Comment: Minor changes and journal-re

Lie symmetries and exact solutions of first-order difference schemes