# Polynomial Time Nondimensionalisation of Ordinary Differential Equations via their Lie Point Symmetries

1 CAFE - Computer algebra and functional equations
CRISAM - Inria Sophia Antipolis - Méditerranée
2 ALIEN - Algebra for Digital Identification and Estimation
Inria Lille - Nord Europe, Inria Saclay - Ile de France, Ecole Centrale de Lille, X - École polytechnique, CNRS - Centre National de la Recherche Scientifique : UMR8146
Abstract : Lie group theory states that knowledge of a~$m$-parameters solvable group of symmetries of a system of ordinary differential equations allows to reduce by~$m$ the number of equation. We apply this principle by finding dilatations and translations that are Lie point symmetries of considered ordinary differential system. By rewriting original problem in an invariant coordinates set for these symmetries, one can reduce the involved number of parameters. This process is classically call nondimensionalisation in dimensional analysis. We present an algorithm based on this standpoint and show that its arithmetic complexity is polynomial in input's size.
Mots-clés :
Document type :
Other publications

Cited literature [12 references]

https://hal.inria.fr/inria-00001251
Contributor : Alexandre Sedoglavic <>
Submitted on : Wednesday, April 12, 2006 - 4:15:29 PM
Last modification on : Thursday, February 21, 2019 - 10:52:45 AM
Long-term archiving on : Saturday, April 3, 2010 - 11:10:42 PM

### Citation

Évelyne Hubert, Alexandre Sedoglavic. Polynomial Time Nondimensionalisation of Ordinary Differential Equations via their Lie Point Symmetries. 2006. ⟨inria-00001251⟩

Record views