Stability of time discretizations for semi-discrete high order schemes for time-dependent PDEs

Department of Mathematics Colloquium

Meeting Details

For more information about this meeting, contact Kristin Berrigan, Stephanie Geyer, Sergei Tabachnikov, Dmitri Burago, Alberto Bressan, Nigel Higson.

Speaker: Chi-Wang Shu, Brown University

Abstract: When designing high order schemes for solving time-dependent PDEs, we often first develop semi-discrete schemes paying attention only to spatial discretizations and leaving time $t$ continuous. It is then important to have a high order time discretization to main the stability properties of the semi-discrete schemes. In this talk we discuss several classes of high order time discretization, including the implicit-explicit (IMEX) Runge-Kutta or multi-step time marching, which treats the more stiff term (e.g. diffusion term in a convection-diffusion equation) implicitly and the less stiff term (e.g. the convection term in such an equation) explicitly, for which strong stability can be proved under the condition that the time step is upper-bounded by a constant under suitable conditions, and the explicit Runge-Kutta methods, for which strong stability can be proved in many cases for semi-negative linear semi-discrete schemes. Numerical examples will be given to demonstrate the performance of these schemes.

Room Reservation Information

Room Number: 114 McAllister

Date: 11/21/2019

Time: 3:30pm - 4:30pm