TY - JOUR
T1 - Tailored Finite Point Method for Numerical Solutions of Singular Perturbed Eigenvalue Problems
AU - Han , Houde
AU - Shih , Yin-Tzer
AU - Tsai , Chih-Ching
JO - Advances in Applied Mathematics and Mechanics
VL - 3
SP - 376
EP - 402
PY - 2014
DA - 2014/06
SN - 6
DO - http://doi.org/10.4208/aamm.2013.m376
UR - https://global-sci.org/intro/article_detail/aamm/25.html
KW - Singular perturbation, tailored finite point, Schrödinger equation, eigenvalue problem.
AB - <p style="text-align: justify;">We propose two variants of tailored finite point (TFP) methods for discretizing two dimensional singular perturbed eigenvalue (SPE) problems. A continuation
method and an iterative method are exploited for solving discretized systems of equations to obtain the eigen-pairs of the SPE. We study the analytical solutions of two
special cases of the SPE, and provide an asymptotic analysis for the solutions. The
theoretical results are verified in the numerical experiments. The numerical results
demonstrate that the proposed schemes effectively resolve the delta function like of
the eigenfunctions on relatively coarse grid.</p>