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Discretization of partial differential equations preserving their physical symmetries

Francis Valiquette·Pavel Winternitz
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Abstract

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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Francis Valiquette, Pavel Winternitz. 2005-08-05. Discretization of partial differential equations preserving their physical symmetries. https://doi.org/10.1088/0305-4470/38/45/004

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