報告人：周永濤（青島理工大學）

報告題目：A meshless method based on the generalized finite difference method and L1 method for solving a time-fractional advection-diffusion equation

報告摘要：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.

報告時間：2024年10月19日（星期六）10:00-12:00

報告地點：科技樓南706室

邀請人：張誠堅

報告人簡介：周永濤，青島理工大學理學院副教授, 碩士生導師，2019年12月畢業于88858cc永利獲理學博士學位，随後于2020年3月至2023年3月在北京計算科學研究中心數學學科從事博士後研究工作，後于2023年5月就職于青島理工大學。主要從事分數階微分方程數值解、分數階微分方程快速疊代算法、帶弱奇異核的Volterra積分-微分方程數值解的研究工作。近年來先後主持、參與國家自然科學基金（青年、面上）、山東省自然科學基金（青年）、中國博士後科學基金4項，已發表SCI論文20餘篇。