报告题目：Efficient stability-preserving numerical methods for nonlinear coercive problems in vector space

报告人：王晚生教授 上海师范大学

报告时间：2022年11月25日 10:00-12:40

报告地点：腾讯会议 155 771 310

报告摘要： Strong stability (or monotonicity)-preserving time discretization schemes preserve the stability properties of the exact solution and have proved very useful in scientific and engineering computation, especially in solving hyperbolic partial differential equations. The main aim of this work is to further extend this to exponential stability-preserving numerical methods for general coercive system whose solution is exponentially growing or decaying and the rate of growth or decay can be quantified by a $(\omega,\tau^*)$ function in general vector space with a convex functional. Under the same stepsize condition as for strong stability, sharper exponential stability results are derived for explicit and diagonally implicit Runge-Kutta methods and variable coefficients linear multistep methods for nonlinear problems. The new developments in this paper also include their applications to various linear and nonlinear evolution problems.

王晚生，上海师范大学教授，博导，数理学院副经理。2008年6月博士毕业于湘潭大学，随后在华中科技大学、剑桥大学从事博士后工作，2004年7月-2018年1月在长沙理工大学工作，2018年2月开始在上海师范大学工作。王晚生教授获得湖南省自然科学奖二等奖2项（1项排名第一，1项排名第6）、霍英东青年教师奖等，主持国家自然科学基金项目、湖南省杰青、上海市“科技创新行动计划”基础专项等科研项目。王晚生教授主要从事微分方程数值解方面的研究工作，主要研究兴趣在泛函微分方程数值解、偏微分方程数值解、金融期权快速定价、非线性微分方程保结构算法等方面，创新成果发表在Numer. Math.、SIAM. J. Numer. Anal., Math. Comp., SIAM. J. Sci. Comput, J. Sci. Comput., Adv. Comput. Math.等多个国际计算数学权威期刊上。欢迎广大师生踊跃参加