报告名称：A novel numerical approach to time-fractional parabolic equations with nonsmooth solutions

主办单位：数学与统计学学院

报告专家：李东方

专家所在单位：华中科技大学

报告时间：2019年10月24日下午17：00—18:00点

报告地点：数学与统计学学院203

专家简介：李东方，华中科技大学数学与统计学院教授，博导，中国系统仿真学会仿真算法专业委员会委员。主要从事微分方程数值解、系统仿真和信号处理等方面的研究。曾先后赴加拿大McGill大学，香港城市大学从事博士后研究。截至目前在《SIAM. J. Numer. Anal.》，《SIAM. J. Sci. Comput.》、《J. Comp. Phys.》、《Appl. Comp. Harm. Appl.》等多个国际著名计算学科SCI期刊上发表第一或者通讯作者论文30余篇。主持国家自然科学基金面上项目、青年基金各一项，博士后基金一项，参与多项国家自然科学基金。先后获得华中科技大学学术新人奖、香江学者奖等。

报告摘要：This talk is concerned with construction and analysis of some novel numerical methods for time-fractional parabolic equations. Due to the Caputo time derivative being involved, the solutions of equations are often singular near the initial time t = 0 even for a smooth setting. Based on a simple change of variable, an equivalent s-fractional differential equation is derived and a novel L1 finite difference method is proposed for solving the sfractional differential equation. Under the proved regularity, we show that the proposed L1 method provides the optimal accuracy. Numerical examples for both linear and nonlinear fractional equations are presented in comparison with classical L1 methods on uniform meshes and graded meshes, respectively. Our numerical results clearly show the accuracy and efficiency of the proposed methods.

邀请人：向妮