Towards new schemes: A Lie-group approach of the CBKDV and its derived equations

Emma Hoarau (1) , Claire David (1)

1 LMM - Laboratoire de modélisation en mécanique

The aim of this paper is to propose methods that enable us to build new numerical schemes, which preserve the Lie symmetries of the original differential equations. To this purpose, the compound Burgers-Korteweg-de Vries (\textit{CBKDV}) equation is considered. The particular case of the Burgers equation is taken as a numerical example, and the resulting semi-invariant scheme is exposed.

Mots clés: Finite difference schemes; Lie stability

Domaines: Equations aux dérivées partielles [math.AP]

Emma Hoarau, Claire David. Towards new schemes: A Lie-group approach of the CBKDV and its derived equations. 2008. ⟨hal-00260003⟩