Stability and strong convergence in multiscale methods for spatial stochastic kinetics

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Description:	Engblom, S (Uppsala Universitet) Monday 20th June 2016 - 14:00 to 14:45


Created:	2016-06-28 14:00
Collection:	Stochastic Dynamical Systems in Biology: Numerical Methods and Applications
Publisher:	Isaac Newton Institute
Copyright:	Engblom, S
Language:	eng (English)


Abstract:	Co-authors: Pavol Bauer (Uppsala university), Augustin Chevallier (ENS Cachan), Stefan Widgren (National Veterinary Institute) Recent progress in spatial stochastic modeling within the reaction-transport framework will be reviewed. I will first look at the issues with guaranteeing well-posedness of the involved mathematical and numerical models. Armed with this and the Lax-principle, I will then present an analysis of split-step methods and multiscale approximations, all performed in a pathwise, or "strong" sense. These analytical techniques hint at how effective (i.e. parallel) numerical implementations can be designed. Some fairly large-scale simulations will serve as illustrations of the inherent flexibility of the modeling framework. While much of the initial motivation for this work came from problems in cell biology, I will also highlight examples from epidemics and neuroscience. Related Links http://user.it.uu.se/~stefane - Speakers web-page http://dx.doi.org/10.1137/141000841 - Referenced paper http://dx.doi.org/10.4236/am.2014.519300 - Referenced paper http://arxiv.org/abs/1502.02908 - Referenced accepted paper (preprint)

Abstract:

Co-authors: Pavol Bauer (Uppsala university), Augustin Chevallier (ENS Cachan), Stefan Widgren (National Veterinary Institute)

Recent progress in spatial stochastic modeling within the reaction-transport framework will be reviewed. I will first look at the issues with guaranteeing well-posedness of the involved mathematical and numerical models. Armed with this and the Lax-principle, I will then present an analysis of split-step methods and multiscale approximations, all performed in a pathwise, or "strong" sense. These analytical techniques hint at how effective (i.e. parallel) numerical implementations can be designed.

Some fairly large-scale simulations will serve as illustrations of the inherent flexibility of the modeling framework. While much of the initial motivation for this work came from problems in cell biology, I will also highlight examples from epidemics and neuroscience.

Related Links

http://user.it.uu.se/~stefane - Speakers web-page
http://dx.doi.org/10.1137/141000841 - Referenced paper
http://dx.doi.org/10.4236/am.2014.519300 - Referenced paper
http://arxiv.org/abs/1502.02908 - Referenced accepted paper (preprint)

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