报告人:甘四清（中南大学）

报告人简介: 甘四清, 中南大学二级教授、博士生导师。2001年毕业于中国科学院数学研究所获理学博士学位，2001-2003年在清华大学计算机科学与技术系高性能计算研究所做博士后。主要研究方向为确定性微分方程和随机微分方程数值解法。主持国家自然科学基金面上项目3项， 参加国家自然科学基金重大研究计划集成项目1项。在《SIAM Journal on Scientific Computing》、 《BIT Numerical Analysis》、《Journal of Mathematics Analysis and Applications》、《中国科学》等国内外学术刊物上发表论文80余篇。2005年入选湖南省首批新世纪121人才工程。2014年湖南省优秀博士学位论文指导老师。

报告(一)

报告题目：Numerical approximation of stochastic differential equations with non-global Lipschitz coefficients

报告摘要：In this talk, I will first introduce the motivation of numerical analysis of stochastic differential equations (SDEs) with non-global Lipschitz coefficients. Then I will present our recent work on convergence of numerical methods for such SDEs. Finally, future research topics will be suggested.

报告时间: 2019年4月12日下午4:00-4:45.

报告地点: 科技楼南楼602室

报告（二）

报告题目：A full-discrete exponential Euler approximation of the invariant measure for parabolic stochastic partial differential equations

报告摘要：We discrete the ergodic semilinear stochastic partial differential equations in space dimension d≦3 with additive noise, spatially by a spectral Galerkin method and temporally by an exponential Euler scheme. It is shown that both the spatial semi-discretization and the spatio-temporal full discretization are ergodic. Further, convergence orders of the numerical invariant measures, depending on the regularity of noise, are recovered based on an easy time-independent weak error analysis without relying on Malliavin calculus. To be precise, the convergence order is 1−εin space and 1/2−εin time for the space-time white noise case and 2−εin space and 1−εin time for the trace class noise case in space dimension d=1, with arbitrarily smallε> 0. Numerical results are finally reported to confirm these theoretical findings.

报告时间: 2019年4月12日下午5:00-5:45.

报告地点: 科技楼南楼602室