报告题目 (Title)：Robustness: a desirable property of error estimates for time-fractional initial-boundary value problems(时间分数阶初边值问题误差估计中的爆破现象)
报告人 (Speaker)：Martin Stynes 教授（北京计算科学研究中心）
报告时间 (Time)：2021年10月19日(周二) 9:00
报告地点 (Place)：校本部G507
邀请人(Inviter)：李常品
报告摘要(Abstract)：Time-fractional initial-boundary value problems of the form are considered, whereis a Caputo fractional derivative of order . As , we prove that the solution u converges, uniformly on the space-time domain, to the solution of the classical parabolic initial-boundary value problem where is replaced by . Nevertheless, most of the rigorous analyses of numerical methods for this time-fractional problem have error bounds that blow up as , as we demonstrate. We show that in some cases these analyses can be modified to obtain robust error bounds that do not blow up as .
报告人简介：Martin Stynes obtained his B.Sc and M.Sc. degrees from University College Cork, Ireland, then his PhD degree from Oregon State University, USA in 1977. After some other positions, he was at University College Cork from 1984 to 2012. Since 2013 he has been at Beijing CSRC, where he is a Chair Professor funded by the Chinese Government’s 1000 Talent Plan (Recruitment Program of Foreign Experts). He has worked for many years on the numerical solution of singularly perturbed differential equations; the book on this topic by Roos, Stynes and Tobiska is the standard international reference work (1st edition 1996, 2nd edition 2008). For the last 5 years he has worked mainly on fractional-derivative differential equations and their numerical solution. He is an editor of the journals Advances in Computational Mathematics, Applied Numerical Mathematics, and Computational Methods in Applied Mathematics.