Discretization of partial differential equations preserving their physical symmetries

Details Discretization of partial differential equations preserving their physical symmetries Discretization of partial differential equations preserving their physical symmetries

2005-07-25

arxiv.org/abs/math-ph/0507061v2

Physics

Mathematical Physics

29 pages, 3 figures

Scientific paper

10.1088/0305-4470/38/45/004

A procedure for obtaining a "minimal" discretization of a partial differential equation, preserving all of its Lie point symmetries is presented. "Minimal" in this case means that the differential equation is replaced by a partial difference scheme involving N difference equations, where N is the number of independent and dependent variable. We restrict to one scalar function of two independent variables. As examples, invariant discretizations of the heat, Burgers and Korteweg-de Vries equations are presented. Some exact solutions of the discrete schemes are obtained.

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