报告人：肖爱国（湘潭大学）

报告时间：2025年5月10日（星期六）15:00-17:00    

报告地点：科技楼南楼706会议室  

报告摘要：Many positivity-preserving numerical methods have been developed to solve stochastic differential equations (SDEs) with positive solutions in recent years. A common technique in these methods is transformation, such as the Lamperti or logarithmic transformations. It is widely used in one-dimensional cases. However, an effective method for solving multi-dimensional general SDEs with positive solutions has yet to be established. To fill this gap, we propose a positivity-preserving method combining a novel truncated mapping and a truncated Euler-Maruyama discretization in this paper. The strong and weak convergence of the numerical method is studied under local Lipschitz and integrability conditions. Moreover, we show that this method has the optimal strong convergence order 1/2 and the weak convergence order close to 1 under additional assumptions. Numerical experiments are presented to validate theoretical results.

报告人简介：肖爱国，湘潭大学数学与计算科学学院二级教授、湘潭大学韶峰学者特聘岗位学科带头人、湖南省级重点实验室主任、中国仿真学会仿真算法专业委员会主任委员。 曾任学院副院长、中国仿真学会理事、中国数学会计算数学分会常务理事及《计算数学》和《数值计算与计算机应用》编委等。长期从事微分方程数值方法研究，主持国家863课题和国家自然科学基金面上项目7项等，发表SCI论文100多篇，获教育部和湖南省自然科学二等奖、国家教学成果二等奖、湖南省教学成果一等奖、宝钢教育奖优秀教师奖、湖南省优秀研究生导师等。

邀请人：张诚坚