報告題目：Error analysis for a fractional-derivative parabolic problem on quasi-graded meshes
using barrier functions
報 告 人：孟祥雲 北京交通大學
報告時間：2019年12月13日 9:00-10:00
報告地點：數學樓625
報告摘要：
An initial-boundary value problem with a Caputo time derivative of fractional order between 0 and 1 is considered, solutions of which typically exhibit a singular behaviour at an initial time. For this problem, we give a simple and general numerical-stability analysis using barrier functions, which yields sharp pointwise-in-time error bounds on quasi-graded temporal meshes with arbitrary degree of grading. L1-type and Alikhanov-type discretization in time are considered. In particular, those results imply that milder (compared to the optimal) grading yields optimal convergence rates in positive time. Semi-discretizations in time and full discretizations are addressed. The theoretical findings are illustrated by numerical experiments.
報告人簡介：
孟祥雲，北京交通大學教師，本科畢業于吉林大學計算數學專業，博士畢業于北京大學數學科學學院。主要從事奇異攝動問題、分數階方程等問題的研究。
