On the local and global errors of splitting approximations of reaction-diffusion equations with high spatial gradients

Stéphane Descombes (1) , Marc Massot (2) , Thierry Dumont (3) , Violaine Louvet (3)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées
2 EM2C - Laboratoire d'Énergétique Moléculaire et Macroscopique, Combustion
3 ICJ - Institut Camille Jordan

In this paper we study the approximation by splitting techniques of the ordinary differential equation Udot+A U+B U=0, U(0)=U0 with A and B two matrices. We assume that we have a stiff problem in the sense that A is ill-conditionned and U0 is a vector which is the discretization of a function with a very high derivative. This situation may appear for example when we study the discretization of a partial differential equation. We prove some error estimates for two general matrices and in the stiff case, where the estimates are independent of U0 and the commutator between A and B. This paper is dedicated to Michel Crouzeix.

Mots clés: Splitting approximation errors; Reaction-diffusion equations; High spatial gradients

Domaines: Analyse numérique [math.NA]

Stéphane Descombes, Marc Massot, Thierry Dumont, Violaine Louvet. On the local and global errors of splitting approximations of reaction-diffusion equations with high spatial gradients. International Journal of Computer Mathematics, 2007, 84 (6), pp.749 - 765. ⟨10.1080/00207160701458716⟩. ⟨hal-00175003⟩