報告題目： Mesh-robust stability and convergence of variable-step BDF3 method
報告人：廖洪林 教授
時間：2023年9月22日下午：3:00-4:30
地點：本部■維格堂319
摘要：
The third-order BDF (BDF3) scheme with variable steps are practically useful in time adaptive simulations for nonlinear gradient flows, hyperbolic systems with multiscale relaxation and stiff kinetic equations. We prove that the BDF3 scheme is stable for non-stiff problems if the adjacent step ratios are less than 2.553, and is stable for linear diffusion equations if the adjacent step ratios are less than 1.4877. Numerical tests show that the variable-step BDF3 method is mesh-robust with a desired convergence rate, even if many of step-ratios are much greater than our theoretical limits. Up to now, the theoretical analysis remains incomplete so far, and mysterious to us.
This work is joint with undergradte student Li Zhaoyi, Prof. Tang Tao, and Prof. Zhou Tao.
個人簡介：廖洪林，應用數學博№士，2018年至今任教於南京航空航◎天大學數學學院。2001年在原解放軍︾理工大學獲理學碩士學位，2010年在々東南大學獲理學博士學位，2001-2017年任♀教於原解放軍理工大學、解放軍陸軍工程□大學。學術研究方向為微分方程數值解，目前主要關註我这霸王之道相場以及多相流模型的時間變步長離散與自適應算↓法, 在Math Comp，SIAM J Numer Anal, SIAM J Sci Comput，J Comput Phys, IMA J Numer Anal，Sci China Math等國內外專業期刊上◥發表學術研究論文四十余篇。
邀請人：張亞楠