The Similarity Method for Difference Equations

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Abstract
In this paper, the similarity method is applied to ordinary difference equations. When a system of difference equations admits symmetries, it follows that the order of equations can be reduced. Here, by a symmetry is meant a continuous group which leaves the equations invariant. In particular, when a one-dimensional difference equation admits a symmetry, the equation becomes a linear one and an analytic expression for the solution may be obtained. Two examples are given in the final section.

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