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SUMMARY:Uniform accuracy of implicit-explicit methods for stiff hyperbolic
  relaxation systems and kinetic equations - Ruiwen Shu (University of Oxfo
 rd)
DTSTART:20220523T150000Z
DTEND:20220523T160000Z
UID:TALK173420@talks.cam.ac.uk
DESCRIPTION:Many hyperbolic and kinetic equations contain a non-stiff conv
 ection/transport part and a stiff relaxation/collision part (characterized
  by the relaxation or mean free time $\\varepsilon$). To solve this type o
 f problems\, implicit-explicit (IMEX) methods have been widely used and th
 eir performance is understood well in the non-stiff regime ($\\varepsilon=
 O(1)$) and limiting regime ($\\varepsilon\\rightarrow0$). However\, in the
  intermediate regime (say\, $\\varepsilon=O(\\Delta t)$)\, uniform accurac
 y has been reported numerically for most IMEX multistep methods\, while co
 mplicated behavior of order reduction has been observed for IMEX Runge-Kut
 ta (RK) methods. In this talk\, I will take a linear hyperbolic systems wi
 th stiff relaxation as a model problem\, and discuss how to use energy est
 imates with multiplier techniques to prove the uniform accuracy of IMEX me
 thods. In particular\, I will present my joint works with Jingwei Hu on th
 e uniform accuracy of IMEX backward differentiation formulas (IMEX-BDF) up
  to fourth order\, and that of IMEX-RK methods up to third order.&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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