报告题目 (Title)：α-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
主办部门：理学院数学系
报告摘要：Time-fractional initial-boundary value problems of the form
Dtα u-p∂2 u\/∂x2+cu=f
are considered, where D_t^α u is a Caputo fractional derivative of order α∈(0,1). As α→1^-, 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 D_t^α u is replaced by ∂u\/∂t. Nevertheless, most of the rigorous analyses of numerical methods for this time-fractional problem have error bounds that blow up as α→1^-, 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 α→1^-.
