Trémant, Léopold (2018) Asymptotic analysis and numerical approximation of dissipative multi-scale ODEs with a center manifold PFE - Project Graduation, ENSTA.
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.
|Item Type:||Thesis (PFE - Project Graduation)|
|Subjects:||Mathematics and Applications|
|Deposited By:||Léopold Trémant|
|Deposited On:||07 févr. 2019 09:10|
|Dernière modification:||07 févr. 2019 09:10|
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