数苑博雅讲座（79）：Asymptotic analysis and numerical method for singularly perturbed eigenvalue problems
来源：
发布时间：2026-11-09
报告时间：- 2026 年 11 月 12 日（周四）下午 15:00-16:00
- 报告地点：
- 6 号楼 C204 会议室
- 报告人：
- 黄忠亿
- 报告人单位：
- 清华大学
- 邀请人：
- 王燕
- 摘要：
- We study the asymptotic analysis and numerical method for singularly perturbed eigenvalue problems (SPEPs), which arises in describing the semiclassical limit of the spectrum for the Schrödinger operator. We first make a close asymptotic analysis of the SPEP and prove that, for piecewise smooth potential functions, the eigenvalues converge to the minimum value of the potential functions, and the eigenfunctions are concentrated in the immediate vicinity of the minimal points of the potential functions as \(\varepsilon \to 0\). Then we propose some new schemes based on the tailored finite point method (TFPM) for numerical solutions of SPEPs with higher accuracy. Our numerical examples verify our theory and show the feasibility and efficiency of our methods.
