Discrete derivatives and symmetries of difference equations
  We show on the example of the discrete heat equation that for any given discrete derivative we can construct a nontrivial Leibniz rule suitable to find the symmetries of discrete equations. In this way we obtain a symmetry Lie algebra, defined in terms of shift operators, isomorphic to that of the continuous heat equation. 
D. Levi, J. Negro and M.A. del Olmo