发布时间：2025-10-14
A second-order implicit-explicit (IMEX) method on graded meshes for nonlinear time-fractional reaction-subdiffusion problems
主讲人：周永涛
摘要：In this talk, we deal with the numerical solution of nonlinear time-fractional reaction-subdiffusion initial-boundary value problems; the time derivative is a Caputo fractional derivative of order $\alpha \in (0,1)$. First, the problem is transformed into an equivalent integro-differential equation of Volterra type. For this problem a second-order implicit-explicit (IMEX) time-stepping method is combined with the standard 3-point discretisation of the spatial derivative to compute a numerical solution. Under some reasonable assumptions on the data, it is shown that the solution of this method is $O(N^{-2})$ convergent for $\alpha \in (1/2,1)$ when implemented on suitably graded temporal meshes with N points; this result is a significant improvement on the $O(N^{-(2-\alpha)})$ optimal convergence rate of the well-known L1 scheme. To derive this convergence result a novel error analysis is used, based on subtracting two consecutive steps of our method. Numerical examples are given to illustrate our theoretical result and to provide a comparison with the L1 discretisation. These examples show that $O(N^{-2})$ accuracy is obtained when $\alpha \in (0,1]$; to prove this result when $\alpha\in (0,/1/2]$ remains an open problem.
主讲人简介：周永涛，青岛理工大学理学院副教授、硕士生导师，中国仿真算法专业委员会委员，学术研究聚焦分数阶微分方程数值解、快速迭代算法及带弱奇异核的Volterra积分-微分方程数值解等领域，先后主持、参与国家自然科学基金（青年、面上）、山东省自然科学基金（青年）、中国博士后科学基金等6项，已发表20余篇SCI论文，4项发明专利，参与编著《计算方法》。
邀请人：覃婷婷
时间：2025年10月16日10:00-12:00
地点： 科技楼南楼706室