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

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

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.

Author Details

Houde Han

Yin-Tzer Shih

Chih-Ching Tsai