Dr. Jingna Zhang (Yangzhou University)

唐贻发 研究员

Numerical schemes and convergence analysis for multi-term Caputo tempered fractional stochastic delay integro-differential equations

8月10日（周一）15:30-16:30，南楼602

This report focuses on the numerical schemes for a class of multi-term Caputo tempered fractional stochastic delay integro-differential equations. First, by employing mathematical tools such as the Banach fixed-point theorem, we rigorously establish the existence and uniqueness of solutions to the equation. Then, based on this foundation, we construct a direct Euler-Maruyama (EM) scheme for solving this class of equations. To address the issue of excessive computational cost caused by the accumulation of historical integrals in the direct EM method, we propose a fast EM scheme using a combination of the sum-of-exponentials (SOEs) approximation and the Euler quadrature. Theoretical analysis shows that when the tolerance error in the SOEs approximation is sufficiently small, the strong convergence order of the fast EM scheme matches that of the direct EM scheme, namely min{α_i−0.5, α_i−α_{i-1}}, where α_i and α_i−1 are the highest and sub-highest orders of the fractional derivatives, respectively, and this convergence order is independent of the tempering parameter in the Caputo tempered fractional derivative. Moreover, the fast EM scheme reduces the computational complexity from quadratic to nearly linear level and significantly decreases memory usage, thereby greatly improving computational efficiency. Finally, several numerical experiments validate the accuracy of the theoretical results.

报告人简介：张静娜，扬州大学数学科学学院讲师、硕士生导师。2024年于中国科学院数学与系统科学研究院获计算数学博士学位。主要从事分数阶随机微分方程的数值方法研究，以及机器学习在分数阶微分方程中的应用研究。在 Communications in Nonlinear Science and Numerical Simulation、Applied Numerical Mathematics、Journal of Applied Mathematics and Computing 等期刊发表学术论文10余篇。