演讲人Speaker：

张继伟 教授

题目Title:  

The introduce to numerical methods for subdiffusion equations

时间Date& Time：  

2021 年 6 月 23日      09：00--10：00

地点Venue：  

腾讯会议 ID：641 880 484

内容摘要Abstract：

This talk will first introduce the history of fractional calculus, and present a fast algorithm for the Caputo derivative based on the Sum-of-exponentials (SOE) approximation technique. After that, we introduce the numerical analysis for reaction-diffusion equations with variable time step by taking the widely used L1 scheme for an example. For the stability analysis, the discrete complementary convolution (DCC) kernels are introduced to prove the discrete fractional-type Gronwall inequality. For the convergence analysis, the goals are theoretically challenging because the numerical Caputo formula always has a form of discrete convolutional summation. To circumvent this difficulty, an error convolution structure (ECS) analysis is proposed to express the consistence error for the discrete Caputo formula, which can significantly reduce consistence analysis for general nonuniform time steps. In addition, the technique here is also useful to extend the knowledge to study multi-step schemes such as BDF2 with variable time step for integer-order parabolic equations.

个人简介About the speaker:

张继伟，武汉大学数学与统计学院教授，博士生导师。 2003和2006年在郑州大学获得学士和硕士学位，2009年在香港浸会大学获得博士学位。随后在南洋理工大学和纽约大学克朗所从事博士后研究，2014年5月在北京计算科学研究中心工作，2018年11月到武汉大学工作。主要研究领域包括偏微分方程和非局部模型的数值解法，以及神经科学的建模与计算。主要成果发表在SIAM系列,  Math. Comput.，J. Comput. Neurosci., Plos Comput. Bio.等国际知名期刊上。