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北京计算科学研究中心博士后陈虎应邀来院做学术报告
2019-01-08 16:49     (访问量:)

 

学术报告

 

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

 

报告人:  陈虎博士  

 

报告时间:201919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 the mean square displacement is proportionalto tα with 0 < α < 1. There is much current interest in the constructionand analysis of numerical methods for the solution of such problems, whichtypically exhibit a weak singularity at the 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 that are fitted to the initial weaksingularity. In the IBVP the spatial domain is the unit square, where a spectralmethod is used, but other domains (in Rd for d 1) and other spatialdiscretisations (finite element, finite difference) could be handled bymodifying our analysis.  

 

It is proved in [1] that, when the fitted temporal mesh is chosensuitably, the scheme attains order 3 − α convergence in the discrete L norm for the1-dimensional IVP, and second-order convergence in L(L2) for the IBVP.Numerical results demonstrate the sharpness of these theoretical 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. Math. Comput. Math. 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。

 

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