Release time:2021-10-26 Hits:
- DOI number:10.1137/17M1136249
- Journal:SIAM Journal on Scientific Computing
- Key Words:eigenvalue problem, singular perturbation, asymptotic analysis, tailored finite point method
- Abstract:In this paper, we study the asymptotic analysis and numerical method for singularly perturbed eigenvalue problems (SPEPs). 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 V(x), and the eigenfunctions are concentrated in the immediate vicinity of the minimal points of V(x) as \epsilon \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 TFPM.
- Indexed by:Journal paper
- Discipline:Natural Science
- First-Level Discipline:Mathematics
- Document Type:J
- Volume:40
- Issue:5
- Page Number:A3293-A3321
- Translation or Not:no
- Included Journals:SCI
- Correspondence Author:黄忠亿
- Date of Publication:2018-10-04
