报告人:李寿佛（湘潭大学）

报告题目:B-convergence order of canonical implicit midpoint method and comparison of time discretization methods for nonlinear diffusion dominated partial functional differential equations

报告摘要:In this talk, we firstly prove that canonical implicit midpoint method (CaIM) with piecewise linear interpolation and uniform stepsize is optimally B-convergent of order 2. This new result means that for solving nonlinear stiff Volterra functional differential equations (VFDEs), CaIM method can reach higher computational accuracy, and it provides a theoretical foundation for further constructing and researching second order canonical midpoint splitting method (CMPS) for nonlinear composite stiff evolution equations. Then on this basis, we make a careful comparison of the commonly used time discretization methods for nonlinear diffusion dominated partial VFDE problems, theoretical analysis and numerical experiments indicate that CaIM method is in general superior to all other commonly used time discretization methods, such as canonical implicit Euler method (CaIE), canonical trapezoidal method (CaTr), and the 2-stage Lobatto IIIC canonical Runge-Kutta method (CaLob).

报告人简介: 李寿佛，湘潭大学数学与计算科学学院二级教授，博士生导师. 主要从事计算辐射流体动力学、泛函微分方程数值分析、非线性复合刚性发展方程正则分裂算法及其应用软件研究. 曾主持完成国家自然科学基金面上项目8项，合作主持完成国家高技术863课题4项、国家十二五重大专项课题1项，现在研承担国家十三五重大专项课题1项. 出版学术专著2部，在《SIAM J. Sci. Comput.》、《SIAM J. Numer. Anal.》、《Math. Comp.》等重要刊物发表学术论文150余篇，其中SCI论文63篇。曾获教育部科技进步二等奖(2005) 、湖南省自然科学二等奖(2015)、国家新闻出版署全国优秀科技图书奖(1999)、国家自科基金会与中国工程物理研究院(2010) “NSAF联合基金优秀奖”、教育部“全国优秀教师奖” (2007)、湖南省人民政府“徐特立教育奖”(2009)、湖南省教育委员会“优秀教学成果一等奖”(1997) , 并享受国务院政府特殊津贴.

报告时间:2018年5月12日下午3:00-4:00

报告地点: 科技楼南楼702室