报告人: 甘四清（中南大学）

报告题目:  Convergence of numerical methods for stochastic partial differential equations

报告摘要: For semilinear stochastic partial differential equations (SPDEs) with additive noise, we analyze the weak error of a semi-discretization in time by the linear implicit Euler method. The main result reveals how the weak order depends on the regularity of noise and that the order of weak convergence is twice that of strong convergence. In particular, the linear implicit Euler method for SPDEs driven by trace class noise achieves an almost optimal order 1 − ϵ for arbitrarily small ϵ > 0. For nonlinear stochastic partial differential equations (SPDEs) with multiplicative trace class noise, we propose a Runge-Kutta type scheme. The proposed scheme converges with a higher order than the well-known linear implicit Euler scheme. In comparison to the infinite dimensional analog of Milstein type scheme, our scheme is easier to implement and needs less computational effort due to avoiding the derivative of the diffusion function. Numerical examples are reported to support the theoretical results.

报告人简介: 甘四清, 中南大学二级教授、博士生导师,中国仿真算法专业委员会委员。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》等国内外学术刊物上发表论文70余篇。 

报告时间: 2016年12月28日上午9:00-10:00

报告地点: 科技楼南楼702室