报告题目：Sharp error estimate of nonuniform schemes for sub-diffusion and diffusion equations

报告时间：2022年01月21日（星期五）14:00-16:00

报告平台：腾讯会议 ID ： 334-251-415

报告人：张继伟教授 武汉大学

报告内容简介：This talk focuses on the numerical analysis of reaction-sub-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 classical parabolic equations.

报告人简介：张继伟，武汉大学数学与统计学院教授，博士生导师，曾任北京计算数学会理事。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。现主持一项国家自然科学基金面上项目。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。部分成果发表在SIAM Journal on Scientific Computing, SIAM Journal on Numerical Analysis, Mathematics of Computation, Journal of Computational Neuroscience等国际知名期刊上。