走向现代数学学术报告 - 田天海教授（No. 755)

题目：Balanced implicit Patankar–Euler methods for positive solutions of stochastic differential equations

报告人：田天海 教授（澳大利亚莫那什大学）

时间：2024年12月13日 13:30

腾讯会议ID：372-923-319

报告摘要：Stochastic differential equations (SDEs) are a powerful tool to model fluctuations and uncertainty in complex systems. In this talk, we discuss balanced implicit Patankar-Euler methods to ensure positive simulations of SDEs. Instead of considering the addition of balanced terms to explicit methods in existing balanced methods, we attempt the deletion of possible negative terms from the explicit methods to maintain positivity of numerical simulations. The proposed method successfully addresses the issue of divisions with very small denominators in our recently designed stochastic Patankar method. Stability analysis shows that the balanced implicit Patankar-Euler method has much better stability properties than our recently designed composite Patankar-Euler method. Four SDE systems are used to examine the effectiveness, accuracy, and convergence properties of balanced implicit Patankar-Euler methods.

报告人简介：田天海，澳大利亚莫那什大学数学学院教授。2001年在澳大利亚昆士兰大学取得博士学位。其研究领域包括基因网络和细胞信号传导等生物系统的随机建模，随机动力系统的数值模拟，模型参数估计，和统计分析与计算。获得过澳大利亚研究基金会的“未来研究员”（Future Fellow）和“澳大利亚研究员”(Australian Fellow)以及格拉斯哥大学“凯尔文爵士研究员”(Lord Kelvin Fellow)等称号。其研究成果已发表在高级别的学术刊物上，包括“自然杂志细胞生物学分刊”，“美国国家科学院会刊”和“当代生物学”等杂志。共发表150多篇学术论文,其中有100多篇学术论文被SCI收录，被他人SCI引用1700多次。