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Lie group formalism for difference equations. (English) Zbl 0956.39013
The methods of Lie group analysis of differential equations are generalized to provide an infinitesimal formalism for calculating symmetries of difference equations. The authors analyse three linear and one nonlinear examples. For the linear equations, it is found that the symmetry algebra of the discrete equation is isomorphic to that of its continuous limit.
MSC:
39A12Discrete version of topics in analysis
39A10Additive difference equations
34C30Manifolds of solutions of ODE (MSC2000)
43A80Analysis on other specific Lie groups
22E30Analysis on real and complex Lie groups