报告人：周永涛（青岛理工大学）

报告题目：A meshless method based on the generalized finite difference method and L1 method for solving a time-fractional advection-diffusion equation

报告摘要：In this talk, we present a meshless method for solving a time-fractional advection-diffusion equation. The spatial discretization formulas are derived using the generalized finite difference method, and the L1 method is developed to effectively handle the time Caputo derivative. To address the weak singularity of the solution of the time-fractional advection-diffusion equation at the initial time, a graded temporal mesh is employed. The proposed scheme satisfies a discrete comparison principle, which is used to establish an error bound for the computed solution that is O (N^{-2})  in time on graded temporal meshes with N points. Notably, this result exhibits -robustness, remaining stable as . Numerical experiments corroborate the theoretical findings and demonstrate the method's efficiency.

报告时间：2024年10月19日（星期六）10:00-12:00

报告地点：科技楼南706室

邀请人：张诚坚

报告人简介：周永涛，青岛理工大学理学院副教授, 硕士生导师，2019年12月毕业于华中科技大学获理学博士学位，随后于2020年3月至2023年3月在北京计算科学研究中心数学学科从事博士后研究工作，后于2023年5月就职于青岛理工大学。主要从事分数阶微分方程数值解、分数阶微分方程快速迭代算法、带弱奇异核的Volterra积分-微分方程数值解的研究工作。近年来先后主持、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4项，已发表SCI论文20余篇。