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Lie Symmetries and Exact Solutions of First Order Difference Schemes

Miguel A. Rodriguez·Pavel Winternitz
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Abstract

We show that any first order ordinary differential equation with a known Lie point symmetry group can be discretized into a difference scheme with the same symmetry group. In general, the lattices are not regular ones, but must be adapted to the symmetries considered. The invariant difference schemes can be so chosen that their solutions coincide exactly with those of the original differential equation.

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Miguel A. Rodriguez, Pavel Winternitz. 2004-05-28. Lie Symmetries and Exact Solutions of First Order Difference Schemes. https://doi.org/10.1088/0305-4470%2F37%2F23%2F011

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