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Tailored Finite Point Method for Numerical Solutions of Singular Perturbed Eigenvalue Problems

Published online by Cambridge University Press:  03 June 2015

Houde Han ,
Yin-Tzer Shih  and
Chih-Ching Tsai
Houde Han*
Affiliation:
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
Yin-Tzer Shih*
Affiliation:
Department of Applied Mathematics, National Chung Hsing University, Taichung 40227, Taiwan
Chih-Ching Tsai*
Affiliation:
Department of Applied Mathematics, National Chung Hsing University, Taichung 40227, Taiwan
*
Email: hhan@math.tsinghua.edu.cn
Corresponding author. Email: yintzer shih@nchu.edu.tw
Email: jet.tsai98004@gmail.com
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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.

Keywords

65N2535B2574G1581Q05Singular perturbationtailored finite pointSchrödinger equationeigenvalue problem
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 6 , Issue 3 , June 2014 , pp. 376 - 402
Copyright
Copyright © Global-Science Press 2014

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