Year: 2014
Author: Houde Han, Yin-Tzer Shih, Chih-Ching Tsai
Advances in Applied Mathematics and Mechanics, Vol. 6 (2014), Iss. 3 : pp. 376–402
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.2013.m376
Advances in Applied Mathematics and Mechanics, Vol. 6 (2014), Iss. 3 : pp. 376–402
Published online: 2014-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
Keywords: Singular perturbation tailored finite point Schrödinger equation eigenvalue problem.