报告人: 王晚生（上海师范大学）

报告人简介: 王晚生，上海师范大学教授，博士生导师。2008年6月博士毕业于湘潭大学，2010年6月从申博sunbet官网数学博士后流动站出站，2004年7月-2018年1月在长沙理工大学工作，2018年2开始在上海师范大学工作。现兼任中国系统仿真学会仿真算法专业委员会委员、湖南省数学会常务理事。一直从事泛函微分方程数值解、偏微分方程快速自适应算法、期权快速定价等方面的研究，在《Numer. Math.》、《SIAM J. Numer. Anal.》、《SIAM J. Sci. Comput.》等计算数学重要期刊上发表SCI收录论文50余篇，获湖南省自然科学奖二等奖2项、霍英东青年教师奖三等奖、中国计算数学学会2009年优秀青年论文竞赛二等奖等。主持国家自然科学基金项目3项、湖南省自然科学基金杰出青年基金项目1项、湖南省教育厅重点项目1项、中国博士后基金特别资助和面上资助等科研项目。2010年9月-2011年6月访问北京大学数学院，2012年10月-2013年1月获美国数学会的Ky and Yu-Fen Fan基金资助访问美国加州大学尔湾分校，2013年8月-2014年7月年由国家留学基金委资助访问剑桥大学应用数学与理论物理系。此外，入选湖南省新世纪“121人才工程”第二层次人选、湖南省普通高校学科带头人、长沙理工大学“青年英才支持计划”人选。

报告题目（一）On the variable two-step IMEX BDF method for parabolic integro- differential equations with nonsmooth initial data arising in finance

报告摘要：In this talk，the implicit-explicit (IMEX) two-step backward differentiation formula (BDF2) method with variable step-sizes, due to the non-smoothness of the initial data, is developed for solving parabolic partial integro-differential equation (PIDE), which describes the jump-diffusion option pricing model in finance. It is shown that the variable step-sizes IMEX BDF2 method is stable for abstract PIDE under suitable time step restrictions. Based on the time regularity analysis of abstract PIDE, the consistency error and the global error bounds for the variable step-sizes IMEX BDF2 method are provided. After time semi-discretization, spatial differential operators are treated by using finite difference methods and the jump integral is computed using the composite trapezoidal rule. A local mesh refinement strategy is also considered near the strike price because of the non-smoothness of the payoff function. Numerical results illustrate the effectiveness of the proposed method for European and American options under jump-diffusion models.

报告时间: 2019年4月20日（星期六）下午2:45-3:45.

报告题目（二）：Two-grid economical algorithms for parabolic integro-differential equations with nonlinear memory

报告摘要：In this talk, several two-grid finite element algorithms for solving parabolic integro-differential equations (PIDEs) with nonlinear memory are presented. Analysis of these algorithms is given assuming a fully implicit time discretization. It is shown that these algorithms are as stable as the standard fully discrete finite element algorithm, and can achieve the same accuracy as the standard algorithm if the coarse grid size $H$ and the fine grid size $h$ satisfy $H=O(h^{\frac{r-1}{r}})$. Especially for PIDEs with nonlinear memory defined by a lower order nonlinear operator, our two-grid algorithm can save significant storage and computing time. Numerical experiments are given to confirm the theoretical results.

报告时间: 2019年4月20日（星期六）下午4:00-5:00.

报告地点: 科技楼南楼702室