报告人：曹婉容（东南大学）

邀请人：李东方

报告时间：2023年8月29日（星期二）16:00-18:00

报告地点：科技楼南楼706室

报告题目：A tamed-Euler method for solving second-order stochastic singular initial value problems under non-global Lipschitz conditions

报告摘要：In this work, we present a tamed-Euler method for second-order stochastic singular initial value problems (SSIVPs) and investigate the strong convergence of the method. Both the singularity at the origin and the nonlinear growth of the coefficients bring big challenges that the classical framework for stochastic differential equations and numerical schemes cannot work. We first prove the existence and uniqueness theorem and the boundedness of the moments of the solution to the SSIVPs under the non-globally Lipschitz condition. Then we present the tamed-Euler method, which is easy-to-implement and efficient. We provide a sharp analysis of the strong convergence of the proposed method, along with the uniform boundedness of numerical solutions. We also apply our results to the stochastic singular Ginzburg-Landau system and provide numerical simulations to illustrate our theoretical findings.

报告人简介：曹婉容，教授，博士生导师，2004年在哈尔滨工业大学数学系获得博士学位后入职东南大学，长期从事随机微分方程、延迟微分方程和分数阶微分方程数值方法的研究。近几年感兴趣的课题是求解随机微分方程和具有非光滑解的分数阶微分方程的高效数值方法，在国际主流计算数学期刊上发表学术论文40余篇，已主持完成或参与完成国家自然科学基金项目4项，目前主持在研国家自然科学基金面上项目1项。