Discretization of partial differential equations preserving their physical symmetries
Mathematical Physics
2009-11-11 v2 math.MP
Exactly Solvable and Integrable Systems
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.
Keywords
Cite
@article{arxiv.math-ph/0507061,
title = {Discretization of partial differential equations preserving their physical symmetries},
author = {Francis Valiquette and Pavel Winternitz},
journal= {arXiv preprint arXiv:math-ph/0507061},
year = {2009}
}
Comments
29 pages, 3 figures