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Journal of Scientific Computing

Erschienen in:

16.03.2017

Tailored Finite Point Methods for Solving Singularly Perturbed Eigenvalue Problems with Higher Eigenvalues

verfasst von: Houde Han, Yintzer Shih, Dongsheng Yin

Erschienen in: Journal of Scientific Computing | Ausgabe 1/2017

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Abstract

We study tailored finite point methods (TFPM) for solving the singularly perturbed eigenvalue (SPE) problems. We first provide an asymptotic analysis for the eigenpairs and show that for some special potential functions when \(\varepsilon \) approaches to zero the square of eigenfunction converges to a Dirac delta function weakly, and the eigenvalue converges to the minimum value of the potential function. For computing the eigenfunction with higher eigenvalue we propose two variants of TFPM for one-dimensional SPE problems and a nonlinear least square TFPM for two-dimensional problems. The eigenfunction with higher eigenvalue can be easily computed on a related coarse mesh on numerical tests, and suggests that the proposed schemes are accurate and efficient for the SPE problems.

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Titel: Tailored Finite Point Methods for Solving Singularly Perturbed Eigenvalue Problems with Higher Eigenvalues
verfasst von: Houde Han
Yintzer Shih
Dongsheng Yin
Publikationsdatum: 16.03.2017
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 1/2017
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-017-0411-1

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