DeepAI AI Chat
Log In Sign Up

Uniformly accurate numerical schemes for a class of dissipative systems

by   Philippe Chartier, et al.
Université de Rennes 1

We consider a class of relaxation problems mixing slow and fast variations which can describe population dynamics models or hyperbolic systems, with varying stiffness (from non-stiff to strongly dissipative), and develop a multi-scale method by decomposing this problem into a micro-macro system where the original stiffness is broken. We show that this new problem can therefore be simulated with a uniform order of accuracy using standard explicit numerical schemes. In other words, it is possible to solve the micro-macro problem with a cost independent of the stiffness (a.k.a. uniform cost), such that the error is also uniform. This method is successfully applied to two hyperbolic systems with and without non-linearities, and is shown to circumvent the phenomenon of order reduction.


page 1

page 2

page 3

page 4


Uniformly accurate schemes for oscillatory stochastic differential equations

In this work, we adapt the micro-macro methodology to stochastic differe...

Why only Micro-F1? Class Weighting of Measures for Relation Classification

Relation classification models are conventionally evaluated using only a...

DeePN^2: A deep learning-based non-Newtonian hydrodynamic model

A long standing problem in the modeling of non-Newtonian hydrodynamics i...

Timing Configurations Affect the Macro-Properties of Multi-Scale Feedback Systems

Multi-scale feedback systems, where information cycles through micro- an...

Approximating Optimal Bidirectional Macro Schemes

Lempel-Ziv is an easy-to-compute member of a wide family of so-called ma...