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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Uniform accuracy of implicit-explicit methods for
stiff hyperbolic relaxation systems and kinetic eq
uations - Ruiwen Shu (University of Oxford)
DTSTART;TZID=Europe/London:20220523T160000
DTEND;TZID=Europe/London:20220523T170000
UID:TALK173420AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/173420
DESCRIPTION:Many hyperbolic and kinetic equations contain a no
n-stiff convection/transport part and a stiff rela
xation/collision part (characterized by the relaxa
tion or mean free time $\\varepsilon$). To solve t
his type of problems\, implicit-explicit (IMEX) me
thods have been widely used and their performance
is understood well in the non-stiff regime ($\\var
epsilon=O(1)$) and limiting regime ($\\varepsilon\
\rightarrow0$). However\, in the intermediate regi
me (say\, $\\varepsilon=O(\\Delta t)$)\, uniform a
ccuracy has been reported numerically for most IME
X multistep methods\, while complicated behavior o
f order reduction has been observed for IMEX Runge
-Kutta (RK) methods. In this talk\, I will take a
linear hyperbolic systems with stiff relaxation as
a model problem\, and discuss how to use energy e
stimates with multiplier techniques to prove the u
niform accuracy of IMEX methods. In particular\, I
will present my joint works with Jingwei Hu on th
e uniform accuracy of IMEX backward differentiatio
n formulas (IMEX-BDF) up to fourth order\, and tha
t of IMEX-RK methods up to third order. \;
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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