Abstract: Volterra delay-integro-differential equations (VDIDEs) arise widely in various scientific fields such as biology, ecology, medicine and physics. This class of equations plays an important role in modeling diverse problems of engineering and natural science, and hence has come to intrigue researchers in numerical computation and theoretical analysis. For VDIDEs, although some researches have been presented, there still exist a lot of open problems keeping to be done both in theory and in computation. Up to now, numerical analyses for VDIDEs were almost all based on the scalar case and the classical Lipschitz condition. In view of this, recently, we developed a series of research for multi-dimensional linear and nonlinear systems of VDIDEs. Where stability theory of systems and their numerical methods were concerned. Some new effective algorithms were derived. In the present talk, the following contents will be introduced:
1. Analytical stability of linear and nonlinear VDIDEs
2. Stability of Pouzet-Runge-Kutta methods for class RI (α, β, σ, γ)
3. Stability and validity of the extended general linear methods for class GRI (α, β, σ, γ) 
  

报告人简介: 张诚坚, 华中科技大学二级教授, 博士生导师. 1998年毕业于湖南大学应用数学专业获理学博士学位, 尔后进入华中科技大学控制科学与工程博士后流动站工作。自1986年7月起, 先后在长沙理工大学、湖南大学及华中科技大学任教，历任助教、讲师、副教授、教授。2002年2月至2004年3月受比利时鲁汶大学科学研究基金资助在该校计算机科学系做合作研究工作。先后担任中国仿真算法专业委员会副主任委员，中国数学学会理事，中国计算数学学会第七、八届常务理事，湖北省数学学会副理事长、"Journal of Applied Mathematics and Statistics"主编、《应用数学》杂志副主编及学术期刊"Contemporary Mathematics and Statistics"、"Abstract and Applied Analysis"、"Acta Mathematica Scientia"、《数学物理学报》、《数学杂志》编委。近年来，主要从事刚性微分方程数值解及其算法理论研究，主持国家自然科学基金面上项目4项，国家自然科学基金重大研究计划子课题、国家高技术研究发展计划(863计划)重点项目子课题、教育部留学回国人员启动基金及湖北省自然科学基金各1项。在"SIAM J. Sci. Comput."、"IMA J. Numer. Anal." 、"Numer. Math."等国内外重要期刊发表学术论文100余篇，其中SCI源期刊论文70余篇，主、参编教材4部，曾获机械工业部科技进步二等奖、湖北省自然科学奖二等奖、湖北省有突出贡献的中青年专家、湖北省优秀教学成果奖一等奖、宝钢优秀教师奖及湖北省优秀教育工作者等，并主持有国家级精品课程及国家视频精品课程。

Date&Time: January 23, 2015 (Friday), 10:30 - 11:30 a.m. 
Location: 606 Conference Room