BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Chi-Wang Shu (Brown University) DTSTART:20210527T130000Z DTEND:20210527T140000Z DTSTAMP:20260423T052709Z UID:SNPDEA/29 DESCRIPTION:Title: Stability of time discretizations for semi-discrete high order schemes for time-dependent PDEs\nby Chi-Wang Shu (Brown University) as part of "P artial Differential Equations and Applications" Webinar\n\n\nAbstract\nIn scientific and engineering computing\, we encounter time-dependent partial differential equations (PDEs) frequently. When designing high order sche mes for solving these time-dependent PDEs\, we often first develop semi-di screte schemes paying attention only to spatial discretizations and leavin g time $t$ continuous. It is then important to have a high order time dis cretization to main the stability properties of the semi-discrete schemes. In this talk we discuss several classes of high order time discretizatio n\, including the strong stability preserving (SSP) time discretization\, which preserves strong stability from a stable spatial discretization with Euler forward\, the implicit-explicit (IMEX) Runge-Kutta or multi-step ti me marching\, which treats the more stiff term (e.g. diffusion term in a c onvection-diffusion equation) implicitly and the less stiff term (e.g. the convection term in such an equation) explicitly\, for which strong stabil ity can be proved under the condition that the time step is upper-bounded by a constant under suitable conditions\, and the explicit Runge-Kutta met hods\, for which strong stability can be proved in many cases for semi-neg ative linear semi-discrete schemes. Numerical examples will be given to d emonstrate the performance of these schemes.\n LOCATION:https://researchseminars.org/talk/SNPDEA/29/ END:VEVENT END:VCALENDAR