ASYMPTOTIC ANALYSIS AND NUMERICAL METHOD FOR SINGULARLY PERTURBED EIGENVALUE PROBLEMS

作者：Kong, Wang; Huang, Zhongyi^*

来源：SIAM Journal on Scientific Computing, 2018, 40(5): A3293-A3321.

DOI：10.1137/17M1136249

• eigenvalue problem
• singular perturbation
• asymptotic analysis
• tailored finite point method

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 V(x), 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 -> 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.

• 出版日期2018
• 单位清华大学