Volume 6, Issue 3
Tailored Finite Point Method for Numerical Solutions of Singular Perturbed Eigenvalue Problems

Houde Han, Yin-Tzer Shih & Chih-Ching Tsai

Adv. Appl. Math. Mech., 6 (2014), pp. 376-402.

Published online: 2014-06

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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

Singular perturbation tailored finite point Schr\"{o}dinger equation eigenvalue problem

  • AMS Subject Headings

65N25 35B25 74G15 81Q05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-6-376, author = {Houde Han, Yin-Tzer Shih and Chih-Ching Tsai}, title = {Tailored Finite Point Method for Numerical Solutions of Singular Perturbed Eigenvalue Problems}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2014}, volume = {6}, number = {3}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2013.m376}, url = {http://global-sci.org/intro/article_detail/aamm/25.html} }
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