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CATEGORIES:Applied Mathematics Seminar Series
SUMMARY:On long time approximation of ergodic stochastic d
ifferential equations\; examples from homogenizati
on and molecular dynamics - Dr Kostas Zygalakis\,
University of Edinburgh
DTSTART:20170220T150000Z
DTEND:20170220T160000Z
UID:TALK2296AT
URL:/talk/index/2296
DESCRIPTION:In this talk we will discuss a variety of differen
t problems related to questions related to the lon
g time behaviour of solutions of stochastic differ
ential equations. This is an important question wi
th relevance in many fields of applied mathematics
\, such as modelling turbulent diffusion and molec
ular dynamics and can be addressed with a variety
of different techniques such as for example homoge
nization. Once the limiting behaviour has been est
ablished\, one needs to design appropriate numeric
al algorithms that are able to capture it correctl
y. This is a very delicate problem and in addressi
ng this\, we will discuss how the recently develop
ed theory of modified equations/backward error ana
lysis for SDEs can explain the behaviour of existi
ng stochastic numerical methods and guide the cons
truction of more efficient ones.\n\nReferences:\n\
nG.A. Pavliotis\, A.M. Stuart\, and K. C Zygalakis
\, Calculating effective diffusivities in the limi
t of vanishing molecular diffusion. J. Comp. Phys
. 228(4) 1030-1055\, (2009).\n\nK.C. Zygalakis\, O
n the Existence and Applications of Modified Equat
ions for Stochastic Differential Equations. SIAM J
. Sci. Comput. 33(1)\, 102-130\, (2011).\n\nG. Iye
r and K. C. Zygalakis. Numerical studies of homoge
nization under a fast cellular flow. Multiscale Mo
del. Simul.\, 10(3):1046-1058\, (2012).\n\nA. Abdu
lle\, G. Villmart\, K. C. Zygalakis. High order nu
merical approximation of the invariant measure of
ergodic SDEs. SIAM J. Num. Anal. 52(4):1600-1622\,
(2014).\nA. Abdulle\, G. Vilmart\, and K.C. Zygal
akis\, Long time accuracy of Lie-Trotter splitting
methods for Langevin dynamics . SIAM J. Numer. A
nal.\, 53(1):1-16\, (2015). \n
LOCATION:Strathcona LT7
CONTACT:David Smith
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