Modified differential equations

Philippe Chartier (1, 2) , Ernst Hairer (3) , Gilles Vilmart (1, 2)

1 IPSO - Invariant Preserving SOlvers
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 Section de mathématiques [Genève]

Motivated by the theory of modified differential equations (backward error analysis) an approach for the construction of high order numerical integrators that preserve geometric properties of the exact flow is developed. This summarises a talk presented in honour of Michel Crouzeix.

Domaines: Analyse numérique [math.NA]

Philippe Chartier, Ernst Hairer, Gilles Vilmart. Modified differential equations. ESAIM: Proceedings, 2007, 21, pp.16-20. ⟨hal-00847919⟩