Schedule

MINDS SEMINAR

MINDS Seminar Series | Adi Ditkowski (Tel Aviv University) - Error Inhibiting Methods with Post-Processing for Ordinary Differe

MINDS SEMINAR
period : 2021-04-20 ~ 2021-04-20
time : 16:00:00 ~ 17:00:00
개최 장소 : Online streaming (Zoom)
Topic : Error Inhibiting Methods with Post-Processing for Ordinary Differential Equations
개요
Date 2021-04-20 ~ 2021-04-20 Time 16:00:00 ~ 17:00:00
Speaker Adi Ditkowski Affiliation Tel Aviv University
Place Online streaming (Zoom) Streaming link ID : 688 896 1076 / PW : letmein
Topic Error Inhibiting Methods with Post-Processing for Ordinary Differential Equations
Contents Efficient high order numerical methods for evolving the solution of an ordinary differential equation are widely used. The popular Runge--Kutta methods, linear multi-step methods, and more broadly general linear methods, all have a global error that is completely determined by analysis of the local truncation error. In prior work in we investigated the interplay between the local truncation error and the global error to construct error inhibiting schemes that control the accumulation of the local truncation error over time, resulting in a global error that is one order higher than expected from the local truncation error. In this talk we extend our error inhibiting framework to include a broader class of time-discretization methods that allows an exact computation of the leading error term, which can then be post-processed to obtain a solution that is two orders higher than expected from truncation error analysis. We define sufficient conditions that result in a desired form of the error and describe the construction of the post-processor. A number of new explicit and implicit methods and IMEX methods that have this property are given and tested on a variety of ordinary and partial differential equation. We show that these methods provide a solution that is two orders higher than expected from truncation error analysis alone.
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