38 citations · 81 across the 15 of their papers we have counts for
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math-ph2005★ 26 cited
Discretization of partial differential equations preserving their physical symmetries
Francis Valiquette, Pavel Winternitz
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…
math-ph2005★ 1 cited
Point transformations in invariant difference schemes
Francis Valiquette
In this paper, we show that when two systems of differential equations admitting a symmetry group are related by a point transformation it is always possible to generate invariant…
math-ph2005★ 3 cited
Discretizations preserving all Lie point symmetries of the Korteweg-de Vries equation
Francis Valiquette
We show how to descritize the Korteweg-de Vries equation in such a way as to preserve all the Lie point symmetries of the continuous differential equation. It is shown that, for a…