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

Preview Full PDF 201 3471
Export citation
  • 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, Schrödinger equation, eigenvalue problem.

  • AMS Subject Headings

65N25, 35B25, 74G15, 81Q05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{AAMM-6-376, author = {}, 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} }
TY - JOUR T1 - Tailored Finite Point Method for Numerical Solutions of Singular Perturbed Eigenvalue Problems 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 -

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.

Houde Han, Yin-Tzer Shih & Chih-Ching Tsai. (2020). Tailored Finite Point Method for Numerical Solutions of Singular Perturbed Eigenvalue Problems. Advances in Applied Mathematics and Mechanics. 6 (3). 376-402. doi:10.4208/aamm.2013.m376
Copy to clipboard
The citation has been copied to your clipboard