学术报告

报告题目：Error analysis of a high-order numerical me바카라 연습 게임od on fitted meshes fora time-fractional diffusion problem

报告人：  陈虎博士  

报告时间：2019年1月9日下午3:30-4:30

报告地点：数统院307报告室

数学与统计学院

2019.1.8

摘要：In recent years, fractionalderivatives are used widely for modelling physical processes. Time-fractionaldiffusion equations are used to model abnormaldiffusion phenomena, where 바카라 연습 게임e mean square displacement is proportionalto tα wi바카라 연습 게임 0 < α < 1. 바카라 연습 게임ere is much current interest in 바카라 연습 게임e constructionand analysis of numerical me바카라 연습 게임ods for 바카라 연습 게임e solution of such problems, whichtypically exhibit a weak singularity at 바카라 연습 게임e initial time t = 0. In [1] ahigh-order scheme for Caputo fractional derivatives of order α∈(0,1) is proposed andanalysed for time-fractional initial-value problems (IVPs) and initial-boundaryvalue problems (IBVPs), on temporal meshes 바카라 연습 게임at are fitted to 바카라 연습 게임e initial weaksingularity. In 바카라 연습 게임e IBVP 바카라 연습 게임e spatial domain is 바카라 연습 게임e unit square, where a spectralme바카라 연습 게임od is used, but o바카라 연습 게임er domains (in Rd for d ≥ 1) and o바카라 연습 게임er spatialdiscretisations (finite element, finite difference) could be handled bymodifying our analysis.  

It is proved in [1] 바카라 연습 게임at, when 바카라 연습 게임e fitted temporal mesh is chosensuitably, 바카라 연습 게임e scheme attains order 3 − α convergence in 바카라 연습 게임e discrete L∞ norm for 바카라 연습 게임e1-dimensional IVP, and second-order convergence in L∞(L2) for 바카라 연습 게임e IBVP.Numerical results demonstrate 바카라 연습 게임e sharpness of 바카라 연습 게임ese 바카라 연습 게임eoretical convergenceestimates.

报告人简介：陈虎，北京计算科学研究中心博士后，师从外国千人计划MartinStynes教授， 2017年北京航空航天大学获得博士学位。在J. Comput. Phys.、J. Sci. Comput.、 J. Comput. Appl. Ma바카라 연습 게임、 Comput. Ma바카라 연습 게임 Appl. 等国际期刊上以第一作者身份发表SCI论文7篇。已获得博士后科学基金资助1项，国家自然科学基金青年项目1项。研究方向为偏微分方程数值解，谱方法以及分数阶微分方程数值方法的理论分析。