École Nationale Supérieure de
Techniques Avancées

Abstract

We first present a class of equations with a center manifold which relax very quickly, and the numerical shortcomings of usual approaches when dealing with this system. Inspired by recent advances in numerical schemes for highly oscillating problems, a new problem is derived from a two-scale decomposition separating the quick and slow dynamics. Non trivial conditions are then found to assure that this new problem is well-posed, with regular and non stiff solutions. We then devise a uniformly accurate numerical scheme, analyse and implement it. Finally the implementation is studied in terms of convergence and performance and is compared to other schemes and approaches.