Lie Symmetries and Exact Solutions of First Order Difference Schemes

Details Lie Symmetries and Exact Solutions of First Order Difference Schemes Lie Symmetries and Exact Solutions of First Order Difference Schemes

2004-02-25

arxiv.org/abs/nlin/0402047v2

Journal of Physics A: Mathematical and General, 37 (2004) 6129-6142

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Minor changes and journal-ref

Scientific paper

10.1088/0305-4470/37/23/011

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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