Time integration algorithm based on divergent series resummation, for ordinary and partial differential equations

Dina Razafindralandy (1) , Aziz Hamdouni (1)

1 LaSIE - Laboratoire des Sciences de l'Ingénieur pour l'Environnement - UMR 7356

Borel's technique of divergent series resummation is transformed into a numerical code and used as a time integration scheme. It is applied to the resolution of regular and singular problems arising in fluid mechanics. Its efficiency is compared to those of classical discretization schemes.

Mots clés: Peturbation method; divergent series; Borel resummation; Fluid Mechanics

Domaines: Géométrie différentielle [math.DG]; Mécanique des fluides [physics.class-ph]; Analyse numérique [math.NA]; Dynamique Chaotique [nlin.CD]

Dina Razafindralandy, Aziz Hamdouni. Time integration algorithm based on divergent series resummation, for ordinary and partial differential equations. Journal of Computational Physics, 2013, 236, pp.56-73. ⟨10.1016/j.jcp.2012.10.022⟩. ⟨hal-02086543⟩